Question

The distance between the foci of the hyperbola $9x^2-16y^2+18x+32y-151=0$ is

• A. $2$
• B. $8$
• C. $10$
• D. $6$

Answer 1

The correct option is C $10$

$9x^2-16y^2+18x+32y-151=0$
$\Rightarrow 9(x^2+2x)-16(y^2-2y)=151$
$\Rightarrow 9(x^2+2x+1)-16(y^2-2y+1)=151-7$
$\Rightarrow \frac{(x+1{)}^2}{16}-\frac{(y-1{)}^2}{9}=1$
$\Rightarrow a^2=16,b^2=9$
$\therefore e=\sqrt{1+\frac{b^2}{a^2}}=\frac{5}{4}$
Therefore distance between focii is $=2ae=\mathrm{2.4.}\frac{5}{4}=10$
Hence, option 'C' is correct