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Question

Let P be a point on the parabola, x2=4y. If the distance of P from the centre of the circle, x2+y2+6x+8=0 is minimum, then the equation of the tangent to the parabola at P, is :

A
xy+3=0
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B
x+4y2=0
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C
x+y+1=0
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D
x+2y=0
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Solution

The correct option is C x+y+1=0
Let P(2t,t2)Centre of the circle : (3,0)y=D2=(2t+3)2+(t20)2For minimum distance, dydt=02(2t+3)2+4t3=0t3+2t+3=0(t+1)(t2t+3)=0t=1P is (2,1)Equation of tangent to the parabola is, xx1=2a(y+y1)x(2)=2×1(y+1)x+y+1=0

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