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Question

If three distinct and real normals can be drawn to y2=8x from the point (a,0), then-

A
a>2
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B
a(2,4)
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C
a>4
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D
none of these
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Solution

The correct option is D a>4
Equation of normal to the parabola is given by,
y+tx=2at+at3
Here a=2 so,
y+tx=4t+2t3
Given it passes through (a,0)
ta=4t+2t3t(2t2a+4)..(1)
Therefore for three distinct normal through (a,0)
equation (1) must have three distinct roots
a+4<0a>4

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