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Find the angle at which the parabolas y^...

Find the angle at which the parabolas `y^2=4x` and `x^2=32 y` intersect.

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Verified by Experts

The correct Answer is:
`tan^(-1)((3)/(5))`
The given parabola intersect at (16,8). The slope of the tangent to the parabola `y^(2)=4x` at (16,8) is given by
`m_(1)=((dy)/(dx))_((16","8))=((4)/(2y))_((16","8))=(2)/(8)=(1)/(4)`
The slope of the tangent to the parabola `x^(2)=32y` at (16,8) is given by
`m_(2)=((dy)/(dx))_((16","8))=((2x)/(32))_((16","8))=1`
`:." "tantheta=|(1-(1)/(4))/(1+(1)/(4))|=(3)/(5)`
`or" "theta=tan^(-1)((3)/(5))`
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