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Through a fixed point (h,k), secant are ...

Through a fixed point (h,k), secant are drawn to the circle `x^(2)+y^(2)=r^(2)`. Show that the locus of the midpoints of the secants by the circle is `x^(2)+y^(2)=hx+ky`.

Text Solution

Verified by Experts

From the diagram,
`CM _|_BP`
`:. ((y_(1))/(x_(1)))((y_(1)-k)/(x_(1)-h))= -1`

So, the locus of M is
`x^(2)+y^(2)=hx+ky`
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