Question

Find the value of k if x + y + 5 = 0 is a tangent to the circle $x^2+y^2+10x+2ky+10=0$

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is D

None of these

If L is a tangent OP, the perpendicular distance of centre O from L will be equal to radius.

$\Rightarrow OP=\left|\frac{c}{\sqrt{1^2+3^2}}\right|=\left|\frac{c}{\sqrt{10}}\right|$

We have $OP=r=\sqrt{10}$

$\Rightarrow \left|\frac{c}{\sqrt{10}}\right|=\sqrt{10}$

$\Rightarrow \frac{c}{\sqrt{10}}=\pm \sqrt{10}$

$\Rightarrow c=\pm 10$