Question

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

• A. 16,9
• B. 8,6
• C. 4,3
• D. 18,8

Answer 1

The correct option is B

8,6

$9x^2-16y^2+72x-32y-16$ = 0

$\Rightarrow$ 9 ( $x^2$ + 8x) - 16($y^2$ + 2y) = 16

$\Rightarrow$ $9(x+4{)}^2-16(y+1{)}^2=144-16+16$

$\Rightarrow$ $\frac{(x+4{)}^2}{16}-\frac{(y+1{)}^2}{9}=1$

a = 4 $\Rightarrow$ 2a = 8

b = 3 $\Rightarrow$ 2b = 6