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Question

A tangent is drawn at a point on the parabola y2=10x. If this tangent intersect the parabola y2=10x+p at 2 points; then,

A
10<p<10
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B
p<0
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C
p>0
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D
p = 0
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Solution

The correct option is C p>0

Lets draw the given parabola and line

The tangent line is always situated outside the parabola. The second parabola y2=10x+p or y2=10(x+p10) is the same parabola displaced horizontally by p10 units. If the tangent meets the second parabola at 2 points then the displacement should be towards the left

i.e., p10>0

i.e.,p>0


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