The angle between the curves y2=4x and x2=2y−3 at the point (1,2) is
A
60∘
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B
30∘
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C
90∘
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D
0∘
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Solution
The correct option is D0∘ Let the slope of the tangent to the curves at the point of intersection be m1,m2
Slope of tangent for y2=4x at (1,2) is 2ydydx=4 ⇒dydx=2y =m1=1⋯(i)
Similary, slope of tangent to x2=2y−3 2x=2dydx ⇒dydx=x
⇒m2=1 ∴m1=m2=1 ⇒ slope of the tangents are equal and both passes through the point (1,2) ,Hence the tangents coincide ⇒ Angle between them is 0∘