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  • If the curve  intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at t

If the curve x^2 + 2y^2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line segment PQ at the origin is :
Option: 1 \frac{\pi}{2}+\tan ^{-1}\frac{1}{3}
Option: 2 \frac{\pi}{2}-\tan ^{-1}\frac{1}{3}
Option: 3 \frac{\pi}{2}-\tan ^{-1}\frac{1}{4}
Option: 4 \frac{\pi}{2}+\tan ^{-1}\frac{1}{4}

Answers (1)

best_answer

Given equation of the curves are 

\\x^2+2y^2=2\\x+y=1

Homogenising above two equation

\\x^{2}+2 y^{2}-2(x+y)^{2}=0\\x^2+2y^2-2x^2-2y^2-4xy=0\\-x^2-4xy=0\\x(x+4y)=0\\\Rightarrow x=0\;\;or\;\;x+4y=0

These are the equation of the line

\text{Angle between the lines}=\frac{\pi}{2}+\tan ^{-1} \frac{1}{4}

 

Posted by

himanshu.meshram

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