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

- 10 < p < 10

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p < 0

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p > 0

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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 $y^{2} = 10 x + p o r y^{2} = 10 (x + \frac{p}{10})$ is the same parabola displaced horizontally by $\frac{p}{10}$ units. If the tangent meets the second parabola at 2 points then the displacement should be towards the left

i.e., $\frac{p}{10} > 0$

i.e., $p > 0$

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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 tangent is drawn at a point on the parabola $y^{2} = 10 x$ . If this tangent intersect the parabola $y^{2} = 10 x + p$ at 2 points; then,