Question

If the length of the tangents from $(a,b)$ to the circles $x^2+y^2-4x-5=0$ and $x^2+y^2+6x-2y+6=0$ are equal, then the value of $10a-2b$ is

• A. $10$
• B. $-11$
• C. $11$
• D. $-10$

Answer 1

The correct option is B $-11$

Given circles are $x^2+y^2-4x-5=0$ and $x^2+y^2+6x-2y+6=0$
Point from where length of tangents are equal lies on the radical axis,
So the radical axis is
$S_1-S_2=0\Rightarrow -10x+2y-11=0$
Putting $(a,b)$ in the equation of radical axis, we get
$\therefore 10a-2b=-11$