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Question

Three normal are drawn from point (5,0) to parabola y2=4x. The centroid of the triangle formed by feet of these three normals is

A
(3,23)
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B
(5,0)
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C
(2,0)
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D
(0,2)
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Solution

The correct option is B (3,23)
Let the equation of any normal
y=tx+2t+t3
(5,0) Passes through Normal
0=5t+2t+t3
t(t23t)=0
t=0 t=±3
y=0 y=3x+2333
x=1,y=0 y=3(x+1)
x=5y=0 y=3(x+5)
x=3y=23 2y=3(4)
y=23
Centroid=(3,23)

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