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Question

The point on the curve y=x2+4 at which the tangent is perpendicular to the line x+2y=3 is

A
(1,5)
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B
(5,1)
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C
(1,5)
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D
(1,5)
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Solution

The correct option is D (1,5)
Given,

y=x2+4

dydx=2x

let the points on the curve be, α,β

dydxα,β=2α=m1

x+2y=3

slope of the above line,

m2=12

we have,

m1m2=1

m1(12)1

m1=2

2α=2

α=1

β=(1)2+4=5

Therefore the point is (1,5)

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