SOLUTION: Find the equation of a hyperbola with center at (0,0) and passing through points (-1,-2) and (3,4)

Question 723547: Find the equation of a hyperbola with center at (0,0) and passing through points (-1,-2) and (3,4)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the equation of a hyperbola with center at (0,0) and passing through points (-1,-2) and (3,4).
***
Standard form of hyperbola with vertical transverse axis with center at origin:

use two given points to set up two equations to solve a and b.
..
4/a^2-1/b^2=1
16/a^2-9/b^2=1
..
16/a^2-4/b^2=4
16/a^2-9/b^2=1
subtract
5/b^2=3
b^2=5/3
..
4/a^2-3/5=1
4/a^2=8/5
a^2=20/8=5/2
..
Equation:
This is an equation of a hyperbola with vertical transverse axis.
note: I tried with a horizontal transverse axis at first but that did not come out right.
RELATED QUESTIONS
write the equation. 1. hyperbola with foci (0,4) and (0,-4) and asymptotes at y=2x 2.... (answered by KMST)

Find an equation of the circle with center at (1, -2) and passing through (7,... (answered by josgarithmetic)

1. Write the equation of the line passing through the points (0, -4) and (-2, 2. Write... (answered by jim_thompson5910)

Write the general and standard form of the equation of the circle satisfying the given... (answered by Alan3354)

Write the equation of the center at point (-2,3) and cruve passing through points (-2,0)... (answered by stanbon)

write an equation for the ellipse passing through (0, 2) and (4, 0) with center at the... (answered by Alan3354,stanbon)

1. Find an equation of a circle passing through the points A(1,2) and B(1,-2) touching... (answered by Alan3354,greenestamps)

Find the equation of the circle (standard form) with center at (3,-4) and passing through (answered by Alan3354)

1. find the equation of the circle in standard form with center at ( -2, 1) and passing... (answered by mouk)