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Question

Consider the circle x2+y2=9 and the parabola y2=8x. They intersect at P and Q in the first and fourth quadrants, respectively. Tangents to the circle at P and Q intersect the x-axis at R and tangent to the parabola at P and Q intersect the x-axis at S.
The ratio of the areas of the triangle PQS and PQR is

A
1:2
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B
1:2
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C
1:4
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D
1:8
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Solution

The correct option is C 1:4
Coordinates of P and Q are (1,22) and (1,22)
Area of PQR=12×42×8=162
Area of PQS=12×42×2=42
Ration of area of triangle PQS and PQR =42162
=14
Therefore ratio is 1:4.

1081626_1187260_ans_8da1076d32f94d48993a409b898ebaa2.png

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