Question

The equation of the chord of the circle $x^2+y^2=r^2$ passing through $(2,3)$ and farthest from the centre is

• A. $x-3y+7=0$
• B. $2x+y-7=0$
• C. $2x+3y-13=0$
• D. $x+y-5=0$

Answer 1

The correct option is C $2x+3y-13=0$

The chord which is farthest from the centre $(0,0)$ and passing through $(2,3)$ is the chord which has midpoint at $(2,3)$, so
$T=S_1\Rightarrow 2x+3y-r^2=2^2+3^2-r^2\Rightarrow 2x+3y-13=0$