Question

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

• A. $y=x+3\sqrt{2}$
• B. $y=x+\sqrt{2}$
• C. $y=x-\sqrt{2}$
• D. $y=x-3\sqrt{2}$

Answer 1

Answer: (A), (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
$\left|\frac{c}{\sqrt{2}}\right|=3\Rightarrow c=\pm 3\sqrt{2}$

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