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Question

Let E denote the parabola y2=8x. Let P=(2,4) and let Q and Q be two distinct points on E such that the lines PQ and PQ are tangents to E. Let F be the focus of E. Then which of the following statements is (are) TRUE?

A
The triangle PFQ is a right - angled triangle
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B
The triangle QPQ is a right - angled triangle
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C
The distance between P and F is 52
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D
F lies on the line joining Q and Q
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Solution

The correct option is D F lies on the line joining Q and Q
E:y2=8x
P:(2,4)


Point P(2,4) lies on directrix (x=2) of parabola y2=8x

So, QPQ=π2 and chord QQ is a focal chord and segment PQ subtends right angle at the focus.

Chord of contact (QQ) T=0
4y=8×x22
y=x2
Clearly, F(2,0) lies on QQ
PF=(2+2)2+42=42

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