Normal line Definition and 28 Threads

9. When I do this problem I know my slope is -3 because f'(2)=-3. I then went and substituted and got y+5=-3(x-2) which simplified to y=-3x+1 10. I get lost here because the tangent slope would be 0, which would give me the equation y=-2. The normal means perpendicular and the perpendicular...

Homework Statement Given $$\phi = x^{2} +y^{2}-z^{2}-1 $$ Calculate the unit normal to level surface φ = 0 at the point r = (0,1,0) Homework Equations $$ \hat{\mathbf n} = \frac{∇\phi}{|\phi|}$$ $$ z = \sqrt{x^{2}+y^{2} -1} $$ $$ \mathbf n = (1,0,(\frac{\partial z}{\partial x})_{P})...

Hi All, This question is about vector calculus, gradient, directional derivative and normal line. If the gradient is the direction of the steepest ascent: >> gradient(x, y) = [ derivative_f_x(x, y), derivative_f_y(x, y) ] Then it really confuse me as when calculating the normal line...

why do we consider normal line in expressing a plane,say in ##R^3## ,of the form ## ax + by + cz = d ##? What is the logic behind this normal line selection? Plz provide intuitive explanations.Thanks

Homework Statement A cup is represented by the surface -(z-1)2 + x2 + y2 = 1 and it is on a table represented by the plane z=0 a) find the angle at which the cup intersects the table b) find the equation of the normal line to the cup at the point (0, √2 , 2) c) find the equation the tangent...

Homework Statement [/B] Find the coordinates of the point P on the surface of the paraboloid z=6x2+6y2-(35/6) where the normal line to the surface passes through the point (25/6, (25√22)/6, -4). Note that a graphing calculator may be used to solve the resulting cubic equation. Homework...

Homework Statement Find the equation of the normal line of function f(x,y) = x^2+y^2-1 through points (2,1,4) Homework Equations (x-xo)/f_x = (y-yo)/f_y = (z-zo)/f_z The Attempt at a Solution so... f_x = 2x = 4 f_y = 2y = 2 f_z = ? I don't know how to solve for f_z... here...

Homework Statement The function f(x)=5x2+3e2x is invertible. Give the slope of the normal line to the graph of f-1 at x=3 Homework Equations (f-1)'(x)=1/f'(f-1(x)) The slope of the normal line × the slope of the tangent =-1 So basically I just need to find -f'(f-1(x)) at x=3 The Attempt at a...

Homework Statement Find the equation of each of the normal lines to the curve y = x^3 - 4x that is parallel to the line x + 8y - 8 = 0. Homework Equations Differentiation, y - y1 = m(x - x1) The Attempt at a Solution Well, clearly I start by differentiating y = x^3 - 4x to gey...

Hello, i know how to calculate normal line on point but i don't know how to do this problem. "find an equation of the normal line o the parabola y=x^2-5x+4 tha is parallel to the line x-3y=5."

Where does the normal line to the ellipse x2-xy+y2=3 at the point (-1,1) intersect the ellipse a second time?So I took the derivative of the equation to get: y'=(2x-y)/(x-2y) Then I put (-1,1) into the equation, to get a slope of 1. So, for the normal line I got a slope of -1, which has the...

Homework Statement The line that is normal to the curve x2+2xy-3y2=0 at (5,5) intersects the curve at what other point? 2. The attempt at a solution I differentiated the equation, found the slope of the curve at that point, and I then found the equations for the tangent line and normal...

D is a set of all points (x,y) in R2 distinct from (0,0). I have the funtion f: D --> R which is defined by: f(x,y) = (2xy)/(x2+y2 Im asked to find the equations (in plural) of the tangelnt plane and the normal line to the graph of the function at (1,2) My attempt: I use the tangent plane...

Homework Statement DoCarmo Section 1.5 problem 1 part d. Show that the lines containing n(s) and passing through a(s) [a is the curve, and n(s) is the unit normal vector] meet the z axis under a constant angle of pi/2. Helix: a(s) = (a cos(s/c_, a sin(s/c), b*s/c), so I computed n(s) =...

Homework Statement Where does the normal line to the paraboloid z=x^2+y^2 at the point (1,1,2) intersect the paraboloid a second time? Homework Equations The Attempt at a Solution I found the normal line to be 0=2x+2y-1, but I'm not sure what to do next.

Homework Statement Find equations of the tangent plant and the normal line to x-z=4arctan(yz) at (1+∏, 1, 1) Homework Equations The Attempt at a Solution I took the partials and got fx=0 fy=0 fz=(-4y)/((yz)2+1) so for the plane i got -2z-2=0 and for the normal line I got .5z-2=0...

Homework Statement Prove that every normal line to a sphere passes through the centre of the sphere.Homework Equations Equation of the sphere with it's center at O(a,b,c): (x-a)²+(y-b) ²+(z-c)²=r² or (x-a)²+(y-b) ²+(z-c)²-r² = 0 = F(x,y,z)Parametric equations of the normal line at...

Homework Statement xy +yz + zx = 3 (1,1,1) Homework Equations equation of tangent plane is z-z0 = fx(x0,y0)(x-x0) +fy(x0,y0)(y-y0) The Attempt at a Solution Right, I've been a few of these exercises, however, this is the first one I've seen that equals a number and not "z". So...

Homework Statement Find the lines that are tangent and normal to the curve x^2 + xy - y^2=1 at (2,3) Homework Equations Umm.. first derivative and second derivative? The Attempt at a Solution For the tangent line i found the first derivative and used the implicit differentiation(?)...

find the equation of the normal line to the curve y = -3x^2 at the point (-1,-3). you have to use derivatives. i am not asking for the equation of the tangent line i know that is 6x + 3. please show all the steps. the answer is y = -1/6x - 19/6

Homework Statement Find the points where the normal line to the curve y = sqrt(x - 1) is parallel to the line y = 1 - 2x. The Attempt at a Solution m=-2 y' = 1/2sqrt(x-1) = m = -2 -4sqrt(x-1)=1 sqrt(x-1) = - 1/4 x= 1/16 + 1 x= 17/16 so find y y = sqrt((17/16)-1)) (17/16, 1/4) this is...

Homework Statement Where does the normal line to the parabola y= x - x^2 at the point (1,0) intersect the parabola a second time? Illustrate with a sketch Homework Equations y= x - x^2 The Attempt at a Solution y' = 1-2x slope of tangent = -1 (after substituting value of x in...

Homework Statement Find the equation, in standard form, of the normal line drawn to the graph of y=3x4 - 1/x at x = 1 Homework Equations The Attempt at a Solution -I figured out the slope of the tangent to be 12x3 + 1, then at x = 1 the slope is 13 -SO the slope of the...

Homework Statement Find an equation of the normal line to the parabola y = x^2 - 5x + 4 that is parallel to the line x - 3y = 5. Homework Equations ? All that is relevant is mentioned below AFAIK. The Attempt at a Solution Here is my attempt: http://screencast.com/t/oXxI6JPHv My...

Homework Statement I have two problems that don't seem to match. The task is to find the parametric equation for the normal line to the tangent plane. I'm seeing that the vector value of "z" is (-1) with one formula, but not in the other. These two seem to be the same, but the first was solved...

Homework Statement Find the equation of the normal line to the curve y(sqrd) - x(sqrd)y + 3 = 0 at the point (-2,3). (standard form) Homework Equations y - y = m(x - x) The Attempt at a Solution dy __ = -6 dx y - 3 = -6(x + 2) 6x + y +9 = 0

What is the difference between a normal line and a tangent line?

Here is what I found, look at the end to see what my question is: At what point does the normal line to the graph of y= -4 - 3x + 4x^2 at (1, -3 ) intersect the parabola a second time? So far I have tried to find the derivative of the parabola which is: 8x-3 (this corresponds to the...