The equation of director circle of the hyperbola -x2a2- y2b2-1- if b-a- is

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Question

The equation of director circle of the hyperbola $- \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ , if $b > a$ , is

x^{2} + y^{2} = b^{2} - a^{2}

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x^{2} + y^{2} = b^{2}

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x^{2} + y^{2} = a^{2}

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x^{2} + y^{2} = b^{2} + a^{2}

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Solution

The correct option is A $x^{2} + y^{2} = b^{2} - a^{2}$
The equation of director circle whose center us at origin and radius $\sqrt{a^{2} - b^{2}}$
So, $x^{2} + y^{2} = a^{2} - b^{2}$
If $b > a$ , then the equation of director circle of the hyperbola will be $x^{2} + y^{2} = b^{2} - a^{2}$ , where radius will be $\sqrt{b^{2} - a^{2}}$ .

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The equation of director circle of the hyperbola −x2a2+y2b2=1, if b>a, is

The correct option is A x2+y2=b2−a2The equation of director circle whose center us at origin and radius √a2−b2So, x2+y2=a2−b2If b>a, then the equation of director circle of the hyperbola will be x2+y2=b2−a2, where radius will be √b2−a2.

The equation of director circle of the hyperbola $- \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ , if $b > a$ , is