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Question

If the line ky − 2x − k2 + 2h = 0 & parabola x2 = 4y touches each other, then


A

k2(k2 + 2h) = 2

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B

k4(k2 + 2h) = 4

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C

k4(k2 + 2h) = 2

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D

k4(k2 + 2h) = 4

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Solution

The correct option is D

k4(k2 + 2h) = 4


Solving these two equations

ky 2x k2 + 2h = 0 - - - - - - - - - (1) & parabola x2 = 4y (2) is

substituting y = x24 in equation (1)

k.x24 2x k2 + 2h = 0

k4x2 2x k2 + 2h

since ,it touches to parabola ;there should be only one root

discriminant (D)=0

b2 4ac = 0

4 4 × (k4).(k2 + 2h) = 0

1 (k4)(k2 + 2h) = 0

k4(k2 + 2h) = 4


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