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

16, 9

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8, 6

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

4, 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

18, 8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

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

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

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

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

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

Join BYJU'S Learning Program