The hyperbola has center $(0,0)$, and goes through the points $(3,1)$ and $(9,5)$ and the coordinate axes are the symmetry axes. The correct answer is $x^2 - 3y^2=6$.
Asked
Active
Viewed 74 times
0
-
4Hi, and welcome! Please share your thoughts on the problem, explaining what you've tried and where you're finding difficulty. This will help people write answers that are appropriate to your question, and people are generally much more willing to help if you indicate your efforts. – Dec 29 '13 at 00:12
-
I do not know where exactly to start. I do not understand the part "for which the coordinate axis are the symmetry axis" – Jake Dec 29 '13 at 00:13
-
I know that the equation of the hyperbola is (x-h)^2/a^2 - (y-k)^2/b^2=1 where center is (h,k) – Jake Dec 29 '13 at 00:17
1 Answers
0
The equation is $\frac{x^2}{a}-\frac{y^2}{b}=1$ for $a,b\neq 0$. Plugging in the two points you end up with two equations:
$9b-a=ab$
$81b-25a=ab$
So $a=\frac{9b}{b+1}$. This give you that $81b(b+1)-225b=9b^2$ so $b(72b-144)=0$. We obtain that $b=2$ and $a=6$ which give the answer you already know.
Kal S.
- 3,781