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Question

Let x=my+c is normal to x2=4y. If k2+mk+m=0 is satisfies by only one real value of k, then value(s) of c is/are

A
0
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B
72
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C
72
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D
64
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Solution

The correct option is B 72
Given parabola is x2=4y and normal is x=my+c
k2+mk+m=0D=0m24m=0m=0,4
When m=0, the equation of normal becomes
x=c
This is normal only when c=0
When m=4, then equation of normal becomes
x=4y+c(1)
Slope of tangent is 4
Now, differentiating the equation of parabola x2=4y
2x=4dydxm=dydx=x2=4x=8y=16
Now, putting (8,16) in equation (1), we get
c=72

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