Tangent is drawn at any point (p, q) on the parabola y 2 = 4ax. Tangents are drawn from any point on this tangent to the circle
x 2 + y 2 = a 2 , such that the chords of contact pass through a fixed point (r, s) then p, q, r s can hold the relation -
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Equation of tangent yq = 2a (x + p)
Let (x 1 , y 1 ) on this tangent then
y 1 q = 2a (x 1 + p)
chord of contact for circle
xx 1 + yy 1 = a 2 passing through (r, s)
rx 1 + sy 1 = a
2 also xx 1 + y 
(x 1 + p) – a
2 = 0
x 1 
+ 
= 0
x 1 (qx + 2ay) + (2apy – a 2 q) = 0
qx + 2ay = 0
2apy = a 2 q
⇒ qpx + a 2 q = 0 ⇒ x = – 
, y = 
so r = – 
and s = 
⇒ 4ps 2 = – rq 2
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