Question

The focus of the centers of the circle such that the point (2,3) is the mid point of the chord 5x+2y=16 is:

• A. 2x-5y+11=0
• B. 2x+5-11=0
• C. 2x+5y+11=0
• D. 2x-5y-11=0

Answer 1

The correct option is A 2x-5y+11=0

Slope of the given chord =$-\frac{5}{2}$

Slope of the line joining the midpoint on the chord and the centre of the circle =$\left(\frac{3+f}{2+g}\right)$

$\left(\frac{5}{2}\right)\left(\frac{3+f}{2+g}\right)=-1$

$⟹15+5f=4+2g$

$⟹$ locus is $2x-5y+11=0$

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