Question

The lengths of the axes of the hyperbola $9x^2-16y^2+72x-32y-16=0$ are

• A. $16,9$
• B. $8,6$
• C. $4,3$
• D. $18,8$

Answer 1

Answer: (B)

$8,6$

$9x^2-16y^2+72x-32y-16=0$
$\Rightarrow 9(x^2+8x)-16(y^2+2y)=16$
$\Rightarrow 9(x^2+8x+16)-16(y^2+2y+1)=16+144-16$
$\Rightarrow 9(x+4{)}^2-16(y+1{)}^2=144$
$\Rightarrow \frac{(x+4{)}^2}{4^2}-\frac{(y+1)}{3^2}=1$
$\Rightarrow a=4,b=3$
Thus length of the axes of the given parabola are $2a$ and $2b$ respectively $i.e$ 8 and 6.
Hence, option 'B' is correct