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Question

Angle between the tangents drawn to y2=4x at the points where it is intersected by the line y=x1 is equal to

A
π4
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B
π3
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C
π6
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D
π2
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Solution

The correct option is D π2
y2=4x and y=x1

y2=(x1)2=4x

x22x+1=4x

x26x+1=0

(6)±364(1)(1)2(1)

6±322=3±22

x1=3+22, x2=322

y1=2+22, y2=222

2ydydx=4

m1=2y1,m2=2y2

tanθ=m2m11+m1m2

=2y12y21+(2y1)(2y2)

=2y22y1y1y2+4

=2[222222]48+4

tanθ=

θ=90o=π2.

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