1.

If three distinct normals are drawn from `(2k, 0)` to the parabola `y^2 = 4x` such that one of them is x-axis and other two are perpendicular, then `k =`A. 1B. `1/2`C. `3/2`D. none of these

Answer» Correct Answer - C
The equation of any normal to `y^(2)=4x` is
`y=mx-2m-m^(3)`
If it passes through (2k, 0), then
`m^(3)+2m(1-k)=0rArrm=0or m^(2)+(1-k)=0`
Clearly, m = 0 gives y = 0 i.e., x-axis as a normal. Other two normals will be prependicular if product of the roots of `m^(2)+2(2-k)=0` is -1 i.e.,
`2(1-k)=-1rArrk=3/2`


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