If two normals to a parabola y 2 = 4ax intersect at right angles then the chord joining their feet passes through a fixed point whose co-ordinates are:
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y 2 = 4ax .....(i)
slopes of the two normals at the points P(t 1 ) and Q(t 2 ) are – t 1 and – t 2 respectively
(–t 1 ) (–t 2 ) = – 1 ⇒ t 1 t 2 = –1
equation of chord joining P(t 1 ) and Q(t 2 ) is
2x – y (t 1 + t 2 ) + 2at 1 t 2 = 0
⇒ 2x – y (t 1 + t 2 ) – 2a = 0
⇒ (2x – 2a) – (t 1 + t 2 ) (y) = 0 .......(ii)
(ii) will always pass through (a, 0)
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