Home
Class 12
MATHS
If the length of the major axis intercep...

If the length of the major axis intercepted between the tangent and normal at a point `P (a cos theta, b sin theta)` on the ellipse `(x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1` is equal to the length of semi-major axis, then eccentricity of the ellipse is

A

`(cos theta)/(sqrt(1-cos theta))`

B

`(sqrt(1-cos theta))/(cos theta)`

C

`(sqrt(1-cos theta))/(sin theta)`

D

`(sin theta)/(sqrt(1-sin theta))`

Text Solution

Verified by Experts

The correct Answer is:
B
Tangent at point `P (a cos theta, b sin theta)` meets x-axis at `(a)/(cos theta)` Normal at point `P(a cos theta, b sin theta)` meets x-axis at `((a^(2)-b^(2)))/(a) cos theta`
According to the equation `(a)/(cos theta) - ((a^(2)-b^(2)))/(a) cos theta =a`
`rArr e^(2) cos^(2) theta =1 - cos theta rArr e = (sqrt(1-cos theta))/(cos theta)`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

  • EQAUTION OF STRAIGHT LINE AND ITS APPLICATION

    CENGAGE PUBLICATION|Exercise DPP 3.2|13 Videos

Similar Questions

Explore conceptually related problems

If any tangent to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 intercepts equal lengths l on the axes, then find l .

The slop of the tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 at the point (a cos theta, b sin theta) - is

What is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 if length of its minor axis is equal to the distance between its foci ?

Find the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 whose latus reactum is half of its major axis.

If the normal at one end of the latus rectum of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 passes through one end of the minor axis, then prove that eccentricity is constant.

The length of major axis of the ellipse 4x^(2) + 9y^(2) = 36 is _

Find the equation of the tangent and normal of the following curve at the specified point : (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at (a cos theta, b sin theta)

Chords of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are drawn through the positive end of the minor axis. Then prove that their midpoints lie on the ellipse.

The area of the parallelogram formed by the tangents at the points whose eccentric angles are theta, theta +(pi)/(2), theta +pi, theta +(3pi)/(2) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is

Extremities of the latera recta of the ellipses (x^2)/(a^2)+(y^2)/(b^2)=1(a > b) having a given major axis 2a lies on