Determine eqn of Hyperbola w/ given vertices and....

[D!ddy]

Hi, I haven't seen a question like this before..

Determine the standard form of the equation of a hyperbola with vertices (+2, 0) and passing through (4,3).

I haven't seen a question where they ask to determine the equation of a hyperbola using points (passing through (4,3)) but the end result I got was

x[sup:3vzf13t7]2[/sup:3vzf13t7] - y[sup:3vzf13t7]2[/sup:3vzf13t7] = 1
4

I think I'm wrong so if anyone could sort this out for me, I would really appreciate it.

Thanks..
Mo

 

[Opalg]

Determine the standard form of the equation of a hyperbola with vertices (+2, 0) and passing through (4,3).

I haven't seen a question where they ask to determine the equation of a hyperbola using points (passing through (4,3)) but the end result I got was

x[sup:21ge85w9]2[/sup:21ge85w9] - y[sup:21ge85w9]2[/sup:21ge85w9] = 1
4

I think I'm wrong so if anyone could sort this out for me, I would really appreciate it.

It's only slightly wrong. The equation of the hyperbola has to have the form
. . . . . . . . . .\(\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\).
The equation \(\displaystyle x^2/4 - y^2 = 1\) has the correct form, and it goes the vertices \(\displaystyle (\pm2,0)\) (so you've got the coefficient of \(\displaystyle x^2\) correct), but it doesn't go through (4,3). If \(\displaystyle x^2/4 - y^2/b^2 = 1\) holds when x=4 and y=3 then \(\displaystyle b^2=3\), so the answer should be
. . . . . . . . . .\(\displaystyle \frac{x^2}{4} - \frac{y^2}{3} = 1\).