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 $a^2=\frac{25}{2},B^2=16$