Question

The distance from the centre of the circle $x^2+y^2=2x$ to the common chord of the circles $x^2+y^2+5x-8y+1=0$ and $x^2+y^2-3x+7y-25=0$ is

• A. $2$
• B. $4$
• C. $\frac{34}{13}$
• D. $\frac{26}{17}$

Answer 1

Answer: (A)

$2$

Centre of the circle $x^2+y^2=2x$ is $(1,0)$.
Common chord of the other two circles is
$8x-15y+26=0$
Distance from $(1,0)$ to $8x-15y+26=0$
$\frac{|8+26|}{\sqrt{{15}^2+8^2}}=2$