Question

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

• A. $2x+3y=13$
• B. $3x+2y=13$
• C. $2x-3y=13$
• D. None of these

Answer 1

Answer: (A)

$2x+3y=13$

Let $(2,3)$ be given point,

$M$ be the middle point of a chord of the circle $x^2+y^2=a^2$ through $P.$

Then, the distance of the centre $O$ of the circle from the chord is $OM.$

and ${\left(OM\right)}^2={\left(OP\right)}^2-{\left(PM\right)}^2$

which is maximum when $PM$ is minimum,

i.e., $P$ coincides with $M,$ the middle point of the chord.

Hence, the equation of the chord is $T=S_1.$

$\Rightarrow 2x+3y-a^2={\left(a\right)}^2+{\left(3\right)}^2-a^2\Rightarrow 2x+3y=13.$