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Question

If y=4x+3 is parallel to a tangent to the parabola y2=12x, then its distance from the normal parallel to the given line is

A
21317
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B
21917
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C
21117
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D
21017
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Solution

The correct option is B 21917
Equation of normal to y2=4ax having slope m is
y=mx2amam3

So, the equation of normal to y2=12x parallel to y=4x+3 is
y=4x2(3)(4)(3)(4)3
y=4x216

Distance between the lines y=4x216 and y=4x+3

=3(216)(4)2+(1)2

=21917

So, the answer is option (B).

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