Home
Class 12
MATHS
Extremities of the latera recta of the e...

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

A

A. `x^(2) = a(a-y)`

B

B. `x^(2) =a(a+y)`

C

C. `y^(2) =a(a+x)`

D

D. `y^(2) =a(a-x)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Let (h,k) be the extremity of L.R.
`:. h = +- ae, k = +- (b^(2))/(a)`
`:. k= +-a (1-e^(2)) = +-a (1-(h^(2))/(a^(2))) = +- (a-(h^(2))/(a))`
On taking + ve sign, we get
`k = a- (h^(2))/(a)`
`rArr (h^(2))/(a) = a -k rArr a-k rArr h^(2) =a (a-k)`.
On taking -ve sign, we get
`k =- a+(h^(2))/(a)`
`rArr h^(2) = a(a+k)`
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 e be the eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 , then e =

If the tangent at any point of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 makes an angle alpha with the major axis and an angle beta with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosbeta/(cosalpha)

Find the eccentric angles of the extremities of the latus recta of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1

show that the length of the focal chord of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which makes an angle theta with the major axis is (2ab^(2))/(a^(2) sin ^(2) theta+ b^(2) cos^(2) theta) unit.

The parametric equations of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 are _

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

The eqation of auxiliary circle of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) = 1 is _

Find the maximum area of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 which touches the line y=3x+2.

Find the equation of the tangent to the ellipse x^2/a^2+y^2/b^2=1 at (x= 1,y= 1) .

If the tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 make angles alphaa n dbeta with the major axis such that tanalpha+tanbeta=gamma, then the locus of their point of intersection is (a) x^2+y^2=a^2 (b) x^2+y^2=b^2 (c) x^2-a^2=2lambdax y (d) lambda(x^2-a^2)=2x y