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Question

The coordinates of the point on the parabola y=x2+7x+2, which is nearest to the straight line y=3x−3 are

A
(2,8)
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B
(1,10)
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C
(2,20)
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D
(1,4)
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Solution

The correct option is D (2,8)
Any point on the parabola is (x,x2+7x+2)
Its distance from the line y=3x3 is given by
P=∣ ∣3x(x2+7x+2)39+1∣ ∣=x2+4x+510=x2+4x+510
( as x2+4x+5>0 for all xR)
dPdx=0x=2.
So, the required point is (2,8).

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