Question

if chords of hyperbola x2-y2=a2 touch the parabola
y2=4ax then the locus of the mid points of these chords is the curve​

Answer 1

Answer:

Let mid point of the chord is p(h,k)

Thus its equation is given by, T=S1

⇒hx−ky=h2−k2⇒y=khx+kk2−h2

Given this line is tangent to the parabola y2=4ax

Thus Using condition of tangency, c=ma

⇒kk2−h2=hak⇒(h−a)k2=h3

Hence required locus is, (x−a)y2=x3