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Question

If the line y3x+3=0 cuts the parabola y2=x+2 at A and B, the PAPB is equal to [If P=3,0)].

A
4(23)3
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B
4(3+2)3
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C
433
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D
2(3+2)3
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Solution

The correct option is B 4(3+2)3
Given, P=(3,0)
Equation of line AB is
x3cos60=y0sin60=r(say)
x=3+r2,yr32
Therefore, point (3+r2,r32) lies on y2=x+2
3r24=3+r2+2
3r24r2(2+3)=0
Let the roots be r1 and r2, then the product
r1×r2=PAPB=∣ ∣ ∣ ∣(2+3)34∣ ∣ ∣ ∣
=4(2+3)3.
705650_670133_ans_82f095410b174b30b4b5c996cb5c6741.png

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