Prove that the locus of a point, which moves so that its distance from a fixed line is equal to the length of the tangent drawn from it to a given circle, is a parabola.

Explanation

Let the fixed circle be `x^(2)+y^(2)=a^(2)` and the line be y=b

Let veriable point P(h,k) be such that PQ = PR.
`:." "b-h=sqrt(h^(2)+k^(2)-a^(2))`
Squaring, we get
`(b-h)^(2)=h^(2)+k^(2)-a^(2)`
`:." "b^(2)-2bx=y^(2)-a^(2)`,
which is equation of locus of point P.
Clearly, this is the equation of parabola.