Question

If x + y + k = 0 is a tangent to the circle $x^2+y^2$ - 2x - 4y + 3 = 0 then k =

• A. $\pm$ 20
• B. –1, – 5
• C. $\pm$ 2
• D. 4

Answer 1

The correct option is B –1, – 5

Radius = Distance from the centre C(1, 2) to x + y + k = 0
$\Rightarrow$ $\sqrt{1+4-3}$ = $\frac{|1+2+k|}{\sqrt{2}}$ $\Rightarrow$ $|k+3|$ = 2 $\Rightarrow$ k + 3 = $\pm$ 2 $\Rightarrow$ k = -1, - 5