Question

The hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2}=1$ passes through the point of intersection of the lines, $7x + 13y - 87 = 0 $ & $5x - 8y + 7 = 0$ & the latus rectum is $32 \sqrt{2} /5$. The value of ab is

• A. $10 \sqrt{2} $
• B. $ 5\sqrt{2} $
• C. $10 \sqrt{3}$
• D. $200$

Answer 1

Answer: (A)

$7x + 13y - 87 = 0$
$5x - 8y + 7 = 0$
On solving we get $(5,4)$
Now let hyperbola$\frac{x^2}{a^2} - \frac{y^2}{b^2}=1$
$\because$ Passes $(5,4)$
$ \therefore \frac{25}{a^2} - \frac{16}{b^2} = 1 $..........(i)
Also $\frac{2b^2}{a} = \frac{32\sqrt{2}}{5}$............(ii)
By (i), (ii) we get $a^2 = \frac{25}{2} , B^2 = 16$