Home
Class 12
MATHS
If the eccentric angles of two points P ...

If the eccentric angles of two points P and Q on the ellipse `x^2/28+y^2/7=1` whose centre is C differ by a right angle then the area of `Delta CPQ` is

A

5

B

6

C

7

D

8

Text Solution

Verified by Experts

The correct Answer is:
C
If P is the point `(a cos theta, b sin theta)`, the coordinates of Q are `(a cos (theta+ (pi)/(2)), b sin (theta + (pi)/(2)))`
i.e., `(-a sin theta, b cos theta)` where `a^(2) = 28, b^(2) =7`

`:.` The area of `Delta CPQ = (1)/(2) |ab cos^(2) theta + ab sin^(2) theta| { :' area = |{(1)/(2)(x_(1)y_(2)-x_(2)y_(2))}|}`
`= (1)/(2)ab`
`= (1)/(2) (sqrt(28)) (sqrt(7)) =7` sq units.
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CENGAGE|Exercise Multiple Correct Answers Type|6 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

  • ELLIPSE AND HYPERBOLA

    CENGAGE|Exercise Question Bank|28 Videos

Similar Questions

Explore conceptually related problems

The points on the ellipse (x^(2))/(25)+(y^(2))/(9)=1 Whose eccentric angles differ by a right angle are

If the eccentric angles of two points P and Q on the ellipse x^2/a^2+y^2/b^2 are alpha,beta such that alpha +beta=pi/2 , then the locus of the point of intersection of the normals at P and Q is

The ecentric angle of the points on the ellipse (x^(2))/(6)+(y^(2))/(2)=1 whose distane from its centre is 2 is/are.

The eccentric angle of a point on the ellipse x^(2)/6 + y^(2)/2 = 1 whose distance from the centre of the ellipse is 2, is

The distance of a point on the ellipse x^2/6 + y^2/2 = 1 from the centre is 2. Find the eccentric angle of the point.

alpha and beta are eccentric angles of two points A and B on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 If P(a cos theta,b sin theta) be any point on the same ellipse such that the area of triangle PAB is maximum then prove that theta=(alpha+beta)/(2)

P and Q are two points on the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2)) =1 whose eccentric angles are differ by 90^(@) , then

Find the eccentric angle of a point on the ellipse (x^(2))/(6)+(y^(2))/(2)=1 whose distance from the center of the ellipse is sqrt(5)

Find the eccentric angle of a point on the ellipse x^2 + 3y^2 = 6 at a distance 2 units from the centre of the ellipse.