Prove that the locus of the center of a circle, which intercepts a chord of given length `2a` on the axis of `x` and passes through a given point on the axis of `y` distant `b` from the origin, is a parabola.

Explanation

From the figure AC=CD
`:." "sqrt(a^(2)+k^(2))=sqrt(h^(2)+(k-b)^(2))`
Squaring, we get
`a^(2)+k^(2)=h^(2)+k^(2)-2bk+b^(2)`
So, equation of locus of point C is `x^(2)-2by+b^(2)=a^(2)`.
Clearly, this is the equation of parabola.