What will be the equation of conjugate of rectangular hyperbola if the equation of rectangular hyperbola $x^{2} - y^{2} = 8 ?$

x^{2} - y^{2} = - 8

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x^{2} - y^{2} = 8

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x^{2} - y^{2} = - 2 \sqrt{2}

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x^{2} - y^{2} = 2 \sqrt{2}

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Solution

The correct option is A $x^{2} - y^{2} = - 8$
Given: Rectangular hyperbola $x^{2} - y^{2} = 8$

To Find: Equation of conjugate of rectangular hyperbola

We know that, the standard equation of a rectangular hyperbola is $x^{2} - y^{2} = a^{2}$ .

Comparing it with the given equation, $a^{2} = 8$ .

The standard equation of conjugate of rectangular hyperbola is $x^{2} - y^{2} = - a^{2}$ .

$∴$ The equation of conjugate of rectangular hyperbola is $x^{2} - y^{2} = - 8$ .

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What will be the equation of conjugate of rectangular hyperbola if the equation of rectangular hyperbola x2−y2=8?

What will be the equation of conjugate of rectangular hyperbola if the equation of rectangular hyperbola $x^{2} - y^{2} = 8 ?$