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 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

Find the the co-ordinates of the point on the ellipse x^2 + 2y^2 =4 whose eccentric angle is 60^@ .

Find the eccentric angles of the ends of latera recta of the ellipse 2x^(2) +4y^(2) = 1 .

Find the coordinates of a point on the ellipse x^(2) + 2y^(2) = 4 whose eccentric angle is 60^(@)

The eccentric angles of the two points P and Q on the ellipse x^2/a^2+y^2/b^2=1(a>b) are theta and phi resp.If the chord PQ makes angle 90^@ with the vertex (a,0)of the ellipse then show that tan(theta/2)tan(phi/2)=-b^2/a^2

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)

If the distrance of a point on the ellipse 4x^(2) +9y^(2) =36 from its centre is 2, then the eccentric angle of the point is-

If the eccentric angles of the any two points P,Q on the ellipse x^2/a^2+y^2/b^2=1 are (alpha+beta) and (alpha-beta) resp.Show that the equation of chord PQ is x/a cosalpha+y/b sinalpha=cosbeta

If (alpha+beta) and (alpha-beta) are the eccentric angles of the points P and Q respectively on the ellipse x^2/25+y^2/9=1 .Show that the equation of the chord PQ is x/5cosalpha+y/3sinalpha=cosbeta

If (alpha +beta ) and (alpha - beta ) are the eccentric angles of the points P and Q respectively on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 show that the equation of the chord PQ is (x)/(a) cos alpha+(y)/(b)sin alpha = cos beta .

Find the locus of middle points of chords of the ellipse x^2/a^2+y^2/b^2=1 which subtend right angles at its centre.