Find the lengths of conjugate axis of the hyperbola $16 x^{2} - 9 y^{2} = 144$ .

6

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Solution

The correct option is C $8$
The given equation of the hyperbola $16 x^{2} - 9 y^{2} = 144$ can be written as $\frac{x^{2}}{9} - \frac{y^{2}}{16} = 1$

By comparing it with standard equation of the hyperbola, we can see $a = 3$ and $b = 4$

For a standard form of the hyperbola we know that length of transverse axis is $2 a$ and length of conjugate axis is $2 b$ .

So the length of the conjugate axis of the given hyperbola is also $= 2 b = 2 \times 4 = 8$

Hence length of conjugate axis is $8$ , so correct option is $C$

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Find the lengths of conjugate axis of the hyperbola 16x2−9y2=144.

Find the lengths of conjugate axis of the hyperbola $16 x^{2} - 9 y^{2} = 144$ .