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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

p < 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

p > 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

p = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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., $p > 0$

Suggest Corrections

Similar questions

Q. 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,

Q. 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,

Q. If the normals drawn at the end points of a variable chord

P Q

of the parabola

y^{2} = 4 a x

intersect at parabola, then the locus of the point of intersection of the tangent drawn at the points

P

and

Q

A tangent is drawn at the point $P (α, β)$ on the parabola $y^{2} = 4 a x$ . This tangent meets a second parabola $y^{2} = 4 a (x + k)$ at A and B, what is the midpoint of AB?

Q. Assertion :The point of intersection of the tangent at three distinct points

A, B, C

on the parabola

y^{2} = 4 x

can be collinear. Reason: If a line

L

does not intersect the parabola

y^{2} = 4 x

, then from every point of the line two tangents can be drawn to the parabola.

Join BYJU'S Learning Program

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,