The equation of director circle of the circle x 2- y 2- a 2 isA- None of these B- x2-y2-4 a2C- x 2- y 2-2 a 2D- x2-y2-2 a2-0

The correct option is D x^2 + y^2 2a^2 = 0Director circle has its radius √(2) times that of radius of the given circle. Hence equation is x^2 + y^2 = 2a^2 . ...

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Standard XII

Mathematics

Director Circle

The equation ...

Question

The equation of director circle of the circle $x^{2} + y^{2} = a^{2}$ is

x^{2} + y^{2} = 4 a^{2}

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

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x^{2} + y^{2} - 2 a^{2} = 0

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None of these

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Solution

The correct option is C $x^{2} + y^{2} - 2 a^{2} = 0$
Director circle has its radius $\sqrt{2}$ times that of radius of the given circle. Hence equation is $x^{2} + y^{2} = 2 a^{2}$ .

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The equation of director circle of the circle x2+y2=a2 is

The correct option is C x2+y2−2a2=0Director circle has its radius √2 times that of radius of the given circle. Hence equation is x2+y2=2a2 .

The equation of director circle of the circle $x^{2} + y^{2} = a^{2}$ is

The correct option is C $x^{2} + y^{2} - 2 a^{2} = 0$
Director circle has its radius $\sqrt{2}$ times that of radius of the given circle. Hence equation is $x^{2} + y^{2} = 2 a^{2}$ .