hyperbolas Definition and 19 Threads

My approach on this; ##\dfrac{x^2}{4}-\dfrac{y^2}{9}=\dfrac{y^2}{4}-\dfrac{x^2}{9}## ##9x^2-4y^2=9y^2-4x^2## ##13x^2-13y^2=0## ##x^2=y^2## Therefore, on substituting back into equation we shall have; ##\dfrac{x^2}{4}-\dfrac{x^2}{9}=1## ##9x^2-4x^2=36## ##5x^2=36## ##x^2=7.2##...

I know the hyperbola of the form x^2/a^2-y^2/b^2=1 and xy=c; but coming across this question I'm put in a dilemma of how to proceed with calculating anything of it - say eccentricity or latus rectum or transverse axis as said. How to generalize a hyperbola (but i don't want a complex derivation...

when an object is thrown horizontally ,after some time when the effect of the applied force is less than the effect of gravity then it changes its path and bends towards the Earth and the path is called a parabola ,then in the same sense how can we define hyperbola?

This question is typically seen in the beginning of a commutative algebra course or algebraic geometry course. Let $V = \mathcal{Z}(xy-z) \subset \mathbb{A}^3$. Here $\mathcal{Z}$ is the zero locus. Prove that $V$ is isomorphic to $\mathbb{A}^2$ as algebraic sets and provide an explicit...

Hi. I studied calculus a while back but am far from a math god. I have been reading around online about hyperbolic geometry in my spare time and had a simple question about the topic. If a straight line in Euclidean geometry is a hyperbola in the hyperbolic plane (do I have that right?)...

A body can describe 3 types of orbits around another (considering only the gravitational force), a elipse, a hyperbole or a parabola. Does the second kepler law (area law) work for hyperboles or parabolas too?

Hi! Let the function be f(x,y)=x^2-2*y^2,which graph is S:z=f(x,y).Which are the contour curves?Are these hyperbolas? :confused: Thanks in advance!:)

find the equation of the tangents to the hyperbola H` with equation \frac{x^2}{25} - \frac{y^2}{16} = 1 at the point (1,4) in an earlier part of the equation we had to prove that a tangent to the a hyperbola in the form of \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 is in the form of a^2m^2 =...

I know hyberbola in spacetime diagram is that curve-like line below the light cone much like the bottom of a bath tub. But what does "hyperbolas of constant t^2 - x^2" represent? Can anyone point to a spacetime diagram or draw it? Thanks. Happy New Year!

Hello experts! Hope all of you will be fine. I have an equation i.e. xy=c And we all know it is hyperbola. Now I say "graph some of the hyperbolas xy=c". Then kindly tell me how can we extract more than 1 graph from this single equation? And you will write the differential equations for...

Homework Statement 1) A hyperbola goes through the point P(6, 2), and one of its asymptotes is the line r: 2x + 5y = 0. Determine its equation. 2) Prove that a line parallel to one asymptote of a hyperbola interesects it in a single point. Homework Equations The Attempt at a...

The template doesn't quite fit my question, so sorry for not using it :/ If I know the distance from the focus to the vertex of a hyperbola, is it possible to find the equation of the hyperbola, assuming the center is at (0,0) on a Cartesian plane? If yes, how do you do so? Using typical...

Finding linear equations for initial conditions has never been a problem from me since is easy to see (x1, y1) and (x2, y2) can be plugged into the slope equation. But what if I'm looking for a parabolic or even a hyperbolic line, how do I then find its equation with the initial condition that...

This problem was suggested by Gokul43201, based on this year's Putnam A2. Suppose that K is a convex set in \mathbb{R}^2 which is contained in the region bounded by the graphs of the hyperbolas xy=1, xy=-1 (so the set is in the inner + shaped region which contains the origin also). What is...

Does the equation (x+1)^2-4y^2 = 0 have asymptotote?? i graphed it and from the graph it does not look like a hyperbola because it seems to intersect at the point x = -1 y = 0 :frown: Thanks HallsofIvy for helpin me with the previous asymptote hyperbola prob

How do u find the asymptotes to hyperbolas?? what are the asymptotes to this equation? -x^2/4 + y^2/8 = 1 i really need help :confused:

Here are two problems that stumped our entire precal class. And we have a test soon, so I would like to be able to know how to work these type of problems. 1. Write the equation of the hyperbola, x^2 + 4xy + y^2 - 12 = 0, in standard form. Okay, I know the formula needs to be x^2/a^2 -...

Hey, I have a couple of _easy_ questions about hyperbolas, but its been a while since I have worked with them and am not able to look them up in my math book currently...if someone could just get me started in the right direction, I would really appreciate it :) Given the equation of the...

This is algebra. I think I missed this part in class. I know a Hyperbola has a conjugate axis, but is this the hyperbolas equivlent of an elipise's minor axis? If so, how do you find the measurement? I'm writing a forumla for a hyprbola in standard form and need to find b^2. Thanks.