The equation of director circle of ${(x - 1)}^{2} + {(y + 2)}^{2} = 2$ is

x^{2} + y^{2} - 4 x + 2 y + 1 = 0

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x^{2} + y^{2} - 4 x + 2 y - 1 = 0

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x^{2} + y^{2} + 4 x + 2 y + 1 = 0

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

x^{2} + y^{2} - 4 x - 2 y + 1 = 0

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Solution

The correct option is A $x^{2} + y^{2} - 4 x + 2 y + 1 = 0$
Director circle is the concentric circle of radius $\sqrt{2}$ times the given circle.
${(x - 1)}^{2} + {(y + 2)}^{2} = 2$
Radius of circle $= \sqrt{2}$
So radius of director circle $= \sqrt{2} \times \sqrt{2} = 2$
Equation of director circle is
${(x - 1)}^{2} + {(y + 2)}^{2} = 2^{2} {(x - 1)}^{2} + {(y + 2)}^{2} = 4 x^{2} + y^{2} - 4 x + 2 y + 1 = 0$
So option $A$ is correct.

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The equation of director circle of (x−1)2+(y+2)2=2 is

The equation of director circle of ${(x - 1)}^{2} + {(y + 2)}^{2} = 2$ is