Question

If $5x-12y+10=0$ and $12y-5x+16=0$ are two tangents
to a circle then radius of the circle is

• A. $1$
• B. $2$
• C. $4$
• D. $6$

Answer 1

The correct option is A $1$

$5x-12y+10=0$ and $12y-5x+16=0$ are two parallel tangent to a circle.
Then distance $be{t}^n$ this two parallel tangents is $2r$.
$\therefore d=\left|\frac{-10-16}{\sqrt{5^2+{12}^2}}\right|=\left|\frac{26}{13}\right|=2$
$\therefore d=2r=2$
$\Rightarrow r=radius=1$