Question

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

• A. -10 < p < 10
• B. p < 0
• C. p > 0
• D. p = 0

Answer 1

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 $y^2=10x+por{y}^2=10(x+\frac{p}{10})$ 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.,$p>0$