Equation of the conjugate axis of the hyperbola $5 x^{2} - 4 y^{2} - 30 x - 8 y - 39 = 0$ is

x - 3 = 0

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y + 1 = 0

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x + 3 = 0

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

y - 1 = 0

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Solution

The correct option is A $x - 3 = 0$
Given hyperbola is $5 x^{2} - 4 y^{2} - 30 x - 8 y - 39 = 0$
$\Rightarrow 5 (x^{2} - 6 x) - 4 (y^{2} + 2 y) = 39$
$\Rightarrow 5 (x^{2} - 6 x + 9) - 4 (y^{2} + 2 y + 1) = 39 + 45 - 4 = 80$
$\Rightarrow \frac{(x - 3)^{2}}{16} - \frac{(y + 1)^{2}}{20} = 1$
Hence conjugate axis is, $x - 3 = 0$

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