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Question

The length of normal chord of parabola y2=4x, which subtends an angle of 90 at the vertex is

A
63 units
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B
72 units
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C
83 units
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D
92 units
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Solution

The correct option is A 63 units
y2=4x
a=1
Let normal be drawn at point P(t2,2t)and other end of normal be Q(t0)
Vertex O=(0,0)

Slope of OP=2t0t20=2t

Slope of OQ=2t00t200=2t0

POQ=902t2t0=1tt0=4 (1)
Also,
t0=t2t4t=t2t2t=tt2=2t=±2t0=22

The coordinates of P are (2,22) or (2,22)
And coordinates of Q are (8,42) or (8,42)

Length of PQ
=62+(62)2=63 units

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