Parabola Definition and 363 Threads

The problem is: Consider the area under the curve f(x)=2x-x2 and above the x axis. Find the equation of the line through the origin that cuts this area into two equal parts.

Greetings, I‘m trying to analyze the given of directrix x = -1, axis y = 2, and latus rectum as 2 I believe there‘s two possibility equations. I‘m not sure for finding the vertex since I got between ( -.5, 0) and origin itself.

Here is the question: I have posted a link there to this thread so the OP can view my work.

Here is the question: I have posted a link there to this thread so the Op can view my work.

Problem: STATEMENT-1: Through (h,h+1), there cannot be more than one normal to the parabola $y^2=4x$, if $h<2$. STATEMENT-2: The point (h,h+1) lies outside the parabola for all $h\neq 1$. A)Statement-1 is True, Statement-2 is True; Statement 2 is a correct explanation for Statement-1...

How do I find the equation of this parabola?? I am given a parabola with a "way line" l: x+y+2 = 0 and focus point F = (1;1). How do I find it's equation? I know I am suppost to shift it in some way and maybe mirror it, not sure how though. Need some help. The equation of a parabole is y^2...

Homework Statement . Find the point in the parabola ##y^2=x##, ##z=0## closest to the plane ##z=x+2y+8## The attempt at a solution. I've solved some problems where I had to find the closest point from a given surface to another point on the space. In this case, I have to find the...

Tangent and normal parabola Homework Statement P is a point 't' on the parabola y^2=4ax and PQ is a focal chord. PT is a tangent at P and QN is a normal at Q. The minimum distance between PT and QN is equal to Homework Equations The Attempt at a Solution I think minimum distance will...

Here is the question: I have posted a link there to this thread so the OP can see my work.

Homework Statement y^2 = x from (0,0) to (1,1) Homework Equations L = ∫√(1+[g'(y)]^2) dy The Attempt at a Solution So this is a problem in my textbook that has been bothering me because I can't seem to come up with the same answer. 1. [bounds 0 to 1] 1/2∫ sec^3θ was obtained...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement y = 16 -x^2 find centroid bounded by x axis Homework Equations x = (1/A) ∫ x(f(x)) dx and (1/A) (1/2)(f(x))^2 dx = y The Attempt at a Solution I just applied it. It is a weird because I would of thought that x would of been at 0. But I didn't get that I x =...

Find the standard form of the equation of the parabola with the given characteristics and vertex at the origin. Passes through the point (-5, 1/8); vertical axis. I know that there is no focus of the parabola or equation given for this problem, so how would I solve this problem? Is the correct...

Find the standard form of the equation of the parabola with the given characteristics and vertex at the origin. Passes through the point (-1, 1/8); vertical axis. I know that there is no focus of the parabola or equation given for this problem, so how would I solve this problem? Is the correct...

Greetings, I am thinking of ways to make a parabolic dish. If you apply vacuum to one side of a flat circular elastic sheet, will it make a parabolic or spherical shape? Thanks

Hi friends I am sticking in solving a parabola equation. Please help me in solving this issue. The problem is as follows - I have given three points which are as follows - These points are lying on a parabola whose equation is Y2 = 4AX If these points are lying on this...

Homework Statement Find the point(s) on the parabola x= y^2-8y+18 closest to (-2,4) Homework Equations The Attempt at a Solution Using the distance formula I found that d^2 = y^4 - 16y^3 + 105y^2 - 328y + 416 after differentiating I have 2d' = 4y^3 - 48y^2 + 210y -328 I'm not...

Homework Statement Determine a function for wire between two poles if the arc of the wire is parabola. For every 75m there is 1m of sag. Homework Equations y = a(x-p)^2 + q The Attempt at a Solution I think that you need to make the lowest point of the wire the origin and hence...

Homework Statement Consider a bead of mass m sliding without friction on a wire that is bent in the shape of a parabola and is being spun with constant angular velocity ω about its vertical axis. Use cylindrical polar coordinates and let the equation of the parabola be ##z = kρ^{2}##. Write...

Hi, I'm trying to find the Acceleration of a ball rolling down on a parabola. If I could find it, then I could integrate it twice and find it's parametric equation given by the time. How could I find this? I tried a few things, but nothing that made any sense. If someone could give me a hint...

There are two railroads, represented by the curves y=(1/2)x2+7, and x2+y2=1. I am supposed to find a straight line connection so that a atrain can get from one curve to the other. I have drawn a simple diagram to help me picture things: http://i50.tinypic.com/2saeccx.png where (a,b) and (c,d)...

We are given the parabola $y \,=\,ax^2$ . . It opens upward, is symmetric to the y-axis, with vertex at the origin $O$. Select any point $P(p,ap^2)$ on the parabola. Construct the perpendicular bisector of $OP$ . . and consider its $y$-intercept, $b.$ | b|...

Advanced Calculus of Several Variables, Edwards, problem II.4.1: Find the shortest distance from the point (1, 0) to a point of the parabola y^{2} = 4x. This is the Lagrange multipliers chapter. There might be another way to solve this, but the only way I'm interested in right now is the...

Homework Statement The parabola y=1/2 x^2 divides the disk x^2+y^2 <or= to 8 into two equal parts. Find the area of both parts. Homework Equations The Attempt at a Solution I have no idea of how to go about solving this. We haven't done any application problems until now and when...

Homework Statement I've got the equation of a parabola y=2x^2-4x+1 with point (-1,7) and a tangent line running through it the point. I'm supposed to find the equation of the line. Simultaneously solve this equation with that of the parabola, place the results in form ax^2+bx+c, and find the...

Hello. The vertex form is y= a(x-h)^2+k, in general. Could it also be defined as y= a(x+h)^2+k? I am wondering about that minus sign. I see no particular use of it. Is it there because of tradition or am i missing something?

25x^2-10x-200y-119=0 Should i divide both sides by 25 and then put y and constant to right side of equation and then complete the square?

1(a) Homework Statement A spaceship travels in a circular orbit around a planet. It applies a sudden thrust and increases its speed by a factor f . If the goal is to change the orbit from a circle to a parabola, what should f be if the thrust points in the tangential direction? 1(b) Is...

A ray of light is coming along the line $y=b$,($b>0$), from the positive direction of the x-axis and strikes a concave mirror whose intersection with the $x-y$ plane is the parabola $y^2 = 4ax$,($a>0$). Find the equation of the reflected ray and show that it passes through the focus of the parabola.

This question was asked in my exam and I could not answer it. I would like to know how it can be solved. If $l$ and $m$ are variable real numbers such that $5l^2+6m^2-4lm+3l=0$, then a variable line $lx+my=1$ always touches a fixed parabola, whose axis is parallel to the x-axis. (a) Find the...

Hello, I wanted to know why the graph of the hyperbolic cosine function (1/2(e^x)+1/2(e^-x)) looks like a parabola. Is there any reason for this? I suppose the individual exponential functions both go to infinity in a symmetric way... but I wanted a better reason :). Thanks, Mathguy

1. I have a ball that is thrown off a 3m high cliff at 20 m/s horizontally, what is the displacement on the X axis, Vf, and tair? (assuming no air resistance) Homework Equations d=Vi*t+(1/2a*t2 The Attempt at a Solution When I tried to solve this problem I couldn't really find an...

Hello guys, please help me, knowing that the parabola passes through the points A(0,1), B(-1,-2) e C(-2,7). How can i find the equation?

Homework Statement A basketball player is standing 9.5 m from the basket, which is at a height of 3.1m. she throws the ball from a initial height of 2m at an angle of 35 degrees above the horizontal. The ball goes through the basket. Determine intial velocity. PS Assume the max height of the...

Homework Statement Three normals are drawn from the point (14,7) to the curve \large y^{2} -16x-8y=0. Find the co-ordinates of the feet of the normals. Homework Equations Converting the equation of parabola in the form of a perfect square I get \large (y-4)^{2}=16(x+1) The Attempt at a...

Can someone please check that everything I have done so far is correct? A particle movies along a parabola with the displacement equation s = 0.5t2. (a graph is shown) ::::Part I:::: Suppose x-component is s = Ct i) indicate direction of velocity vector and acceleration at point R (arbitrary...

Okay I need to rotate a parabola on a cartesian coordinate system, y=x^2 by 90 degrees about the origin (either direction) without using piecewise, or inverse functions. Basically I am trying to use translations and deformations to accomplish this. Anyone thoughts?

How can I "rotate" a parabola. I want to take an image and make it kind of wavy to distort it (like in a capcha form the letters are distorted sometimes with a wave) . So i figure that I could translate the pixels along a parabola. So the function where y=X^{2} would make the image curve...

Homework Statement Alright so I wasn't sure if I should put this in the Calculus section, but just in case that I would need derivatives to solve this I decided I would put this thread here. http://img99.imageshack.us/img99/9351/capturepf.png The Attempt at a Solution I tried finding...

I have a parabola centered at x=0, equation: y = a*x^2 + c, where a is always negative and c always positive. I need to find a way to calculate a and c, if i know: the arc length above the x axis, and the base width, knowing the base width i also know the x-axis intersections x1,2 =...

Homework Statement Essentially there is a power line which must be strung between posts on two mountains which are 1669.602m apart. The first mountain is 5m higher than the second. To overcome tension the wire is strung with a sag, 1m of sag for every 75m, or part thereof. This sag is...

The point P(2, 8) lies on the parabola C with equation y2=4ax. Find a the value of a, b an equation of the tangent to C at P. the value of a is 8, so y^2 = 32x when finding the tangent y = 4\sqrt{2} x^{\frac{1}{2}} so at P \frac{dy}{dx} = \frac{2\sqrt{2}}{\sqrt{2}} so the...

Homework Statement How would you find the displacement of a velocity/time graph when it is in the shape of a parabola? Homework Equations I know Velocity x time = displacement. The Attempt at a Solution I know that velocity x time = displacement, but how do you find the area under...

Given three arbitrary points on a coordinate system, is there a way to derive an equation that forms the single parabola that passes through all three points? I guess firstly you would have to prove that given three points, only a single parabola passes through all three, but judging by the...

So I found the equation for the perpendicular line to the directrix in order to find the vertex, which I got the line y = x that is perpendicular to the directrix, then solved the system of equations to find the common intersection point, which was (1,1). I used the midpoint formula from the...

Here's a equation of a projectile thrown in a parabolic path : y=xtanθ - gx2/2u2cos2θ where x is the corresponding x - coordinate or the range of a projectile at a point , y is the corresponding y - coordinate or the height of projectile at point, θ is the angle made with the horizontal...

I was given the equation: 2sqrt(2)(x+y)^2=7x+9y I need to then: a)Use rotation of axes to show that the following equation represents a parabola b) Find the XY- and xy- coordinates of the vertex and focus c) Find the equation of the directrix in XY- and xy-coordinates Formulas...

Why is the parabola the most bent, concave, effective mirror? What are some properties of a third order mirror (absolute value of x^3)? There is no uniform focal point. Shouldn't shining a light beam along a normal to the x-axis reflect off of the function multiple times? Then take this to the...

If $${\tmmathbf{r}}$$ and $${\tmmathbf{s}}$$ are piecewise smooth paths, which have the same graph, then they are said to be equivalent paths. They either trace out a set of points in the same direction, or in the opposite direction. If they trace out a curve $${C}$$ in the same...

Homework Statement for what values of m does the line with equation y = mx - 12 not intersect or touch the parabola with equation y = 2x^2-x-10. Please show working out & explain. Homework Equations The Attempt at a Solution This question was asked on openstudy and there...