Show that the locus of the midpoints of chords of the prabola which touch the circle is
Let be the midpoint of the chord of the given parabola.
Equation of the chord is
This line touch the circle with centre (0,0) and radius a.
The perpendicualar distance from the centre is equal to the readius,
Squaring on bothsides,we get
Hence the locus of P is