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Length of Tangent and Power of a Point

Assertion :Co...

Question

Assertion :Consider tow circles $C_{1} \equiv x^{2} + y^{2} + 2 x + 2 y - 6 = 0$ and $C_{2} \equiv x^{2} + y^{2} + 2 x + 2 y - 2 = 0$
Two tangents are drawn from a point on the circle $C_{1}$ to the circle $C_{2}$ then tangents always perpedicular Reason: $C_{1}$ is the director circle of $C_{2}$

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$x^{2} + y^{2} + 2 x + 2 y - 2 = 0$
${(x + 1)}^{2} + {(y + 1)}^{2} = 4$
Director circle of the above circle is-
${(x + 1)}^{2} + {(y + 1)}^{2} = 8$
$x^{2} + y^{2} + 2 x + 2 y - 6 = 0$
$∴$ Tangents drawn from any point on the second circle to the first circle are perpendicular
Hence, statement-1 is true and statement-2 explains it.

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