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Question

The point of intersection of normals to the parabola y2=4x at the points whose ordinates are 4 and 6 is

A
(30,21)
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B
(21,30)
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C
(17,19)
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D
(19,17)
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Solution

The correct option is B (21,30)
Parabola is y2=4x
let the points be P(at21,2at1) and Q(at22,2at2).
a=1 then points will be P(t21,2t1) and Q(t22,2t2)
Normals are drawn at P and Q
Given that ordinates of P and Q are 4 and 6 so,
2t1=4t1=2 and 2t2=6t2=3
Now, point of intersection of normals at P(at21,2at1) and Q(at22,2at2) is R(2a+a(t21+t22+t1t2),at1t2(t1+t2))
substitute t1=2 and t2=3, a=1
R(21,30)

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