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Q.

Consider the parabola y2=4x . Let S be the focus of the parabola. A pair of tangents drawn to the parabola from the point P-2,1 meet the parabola at P1 and P2. Let Q1 and Q2be points on the lines SP1 and SP2 respectively such that PQ1 is perpendicular to SP1 andPQ2 is perpendicular to SP2. Then, which of the following is/are TRUE?

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a

PQ1 = 3

b

Q1Q2=3105

c

SQ2 = 1

d

SQ1 = 2

answer is B, C, D.

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Detailed Solution

Slopes of tangents from P(-2, 1)  are -1 and 1/2
points of Contact are p1(4, 4) and p2(1, -2) 
Equation of sp1 is 4x - 3y - 4 = 0
Q1=25,45
Equation of sp2 is x - 1 = 0 
Q2 = (1, 1) 
Now check options 

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