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  4. The locus of the center of the circles such that the point (2,3) is the midpoint of the chord 5 x+2 y=16 is

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Q. The locus of the center of the circles such that the point $(2,3)$ is the midpoint of the chord $5 x+2 y=16$ is

Conic Sections

Solution:

image
Slope of the given line $=-\frac{5}{2}$
or $\left(\frac{5}{2}\right)\left(\frac{3+f}{2+g}\right)=-1$
or $15+5 f=4+2 g$
Therefore, the locus is $2 x-5 y+11=0$.