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Question

# The angle between lines joining the origin to the point of intersecting of the lie √3x+y=2 and the curve y2−x2=4 is

A
tan1(23)
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B
tan1(32)
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C
π6
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D
π2
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Solution

## The correct option is A tan−1(2√3) solve: Given √3x+y=2 and y2−x2=4 To find the angle between the first we have to find the equation of another line. (0,0) is not satisfy the curve So, we have to homogenise it to getpair of straight line.Given eqn. of line is√3x+y=2=>(√3x+y2)2=12from eqn. of curve we gety2−x2=4[√3x+y2]2⇒y2−x2=3x2+y2+2√3xy⇒4x2+2√3xy=0⇒2x[2x+√3y]=0l1:2x=0⇒x=0slope =tanπ2angle with x axis =π2l2:2x+√3y=0y=−2√3x Slope =−2√3 slepe of line l2=−2√3⇒tanθ=−2√3⇒θ=tan−1−2√3 So, the angle between line =π2−tan−12√3 we know that cot−1x+tan−1x=π2⇒π2−tan−1x=cot−1x⇒π2−tan−12√3=cot−12√3 and tan−1x=cot−1(1x)⇒cos−1(2√3)=tan−2(√32)So, tan−1(√32) is the required angle

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