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Question

If the parabolas y2=4x and x2=32y intersect at (16,8) at an angle θ, then the value of θ is .

A
tan1(35)
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B
tan1(53)
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C
tan1(45)
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D
tan1(54)
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Solution

The correct option is A tan1(35)
The slope of the tangent to y2=4x at (16,8) is given by
m1=(dydx)(16,8)=(42y)(16,8)=14
The slope of the tangent to x2=32y at (16,8) is given by
m2=(dydx)(16,8)=(2x32)(16,8)=1
tan θ=(1(1/4)1+(1/4)∣ ∣=35θ=tan1(35) (acute angle)or θ=π tan1(35) (obtuse angle)

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