The equation of tangent parallel to the line $y = x$ drawn to the circle $x^{2} + y^{2} = 9$ is/are

y = x + 3 \sqrt{2}

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y = x + \sqrt{2}

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y = x - \sqrt{2}

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y = x - 3 \sqrt{2}

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Solution

The correct options are
A $y = x + 3 \sqrt{2}$
D $y = x - 3 \sqrt{2}$
Given equation of circle is $x^{2} + y^{2} = 9$
Let the tangent be $y = x + c .$
Now, the distance from centre $C (0, 0)$ to the tangent is equal to the radius
$∣ ∣ ∣ \frac{c}{\sqrt{2}} ∣ ∣ ∣ = 3 \Rightarrow c = \pm 3 \sqrt{2}$

Hence, equation of tangents are
$y = x \pm 3 \sqrt{2}$

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x^{2} + y^{2} = 9

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