Find the equation of the chord of the circle `x^2+y^2=a^2` passing through the point (2, 3) farthest from the center.

Options

A. `2x+3y=13`
B. `3x-y=3`
C. `-2y+4=0`
D. `x-y+1=0`

Answer

C

Explanation

Let P(2, 3) be the given point and M be the mid-point of a chord through P.
In `DeltaOMP`, we have
`OP^(2)=OM^(2)+PM^(2)rArrOM=sqrt(OP^(2)-PM^(2))`
Clearly OM is maximum when PM is minimum i.e. M coincides with P i.e. P is the mid-point of the chord.
Chord PM passes through P(2, 3) and is perpendicular to OM.
So, its equation is `y-3=-(2)/(3)(x-2)` or, `2x+3y=13`.