CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Point Form of Tangent: Ellipse

The line x+y+...

Question

The line x+y+2 = 0 is a tangent to a parabola $y^{2} = 4 a x$ at point A, it intersects the directrix at B and tangent at vertex at C, then (AC $\times$ BC) =

A

8

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

B

4

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

C

12

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

D

16

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

Open in App

Solution

The correct option is A
8

$a m^{2} = l n \Rightarrow a {(1)}^{2} = 1 \times 2 \Rightarrow a = 2$

A = (2, -4), B = (-2, 0), C = (0, -2) $\Rightarrow$ AC . BC = 8

Suggest Corrections

thumbs-up

1

Similar questions

Q. The line x+y+2 = 0 is a tangent to the parabola

y^{2} = 4 a x

at point A, it intersect the directrix at B and tangent at vertex at C, then

(A C) . (B C) =

Q. The line x + y + 2 =0 is a tangent to a parabola

y^{2} = 4 a x

at the point A. If it intersect the directrix at B and tangent at vertex at C, then

Q. Assertion :The tangents at the extremities of a focal cord of the parabola

y^{2} = 4 a x

intersect on the line

x + a = 0

. Reason: The locus of the point of intersection of perpendicular tangents to the parabola is its directrix.

Q. The locus of point of intersection of the two tangents to the parabola

y^{2} = 4 a x

which intercept a given distance

4 c

on the tangent at the vertex is

Q. If tangent to parabola

y^{2} = 4 a x

intersects ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

A

B,

then the locus of point of intersection of tangents at

A

B,

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Line and Ellipse

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Point Form of Tangent: Ellipse

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon