Home
Class 12
MATHS
Let E(1) and E(2) be two ellipses whose ...

Let `E_(1)` and `E_(2)` be two ellipses whose centres are at the origin. The major axes of `E_(1)` and `E_(2)` lie along the x-axis and the y-axis respectively. Let S be the circle `x^(2)+(y-1)^(2)=2`. The straight line `x+y=3` touches the curves `S, E_(1)" and "E_(2)` at P, Q and R respectively. Suppose that `PQ=PR=(2sqrt(2))/(3)`. If `e_(1)` and `e_(2)` are the eccentricities of `E_(1)` and `E_(2)` respectively, then the correct expression (s) is (are)-

A

`e_(1)^(2)+e_(2)^(2)=(43)/(40)`

B

`e_(1)e_(2)=(sqrt(7))/(2sqrt(10))`

C

`|e_(1)^(2)-e_(2)^(2)|=(5)/(8)`

D

`e_(1)e_(2)=(sqrt(3))/(4)`

Text Solution

Verified by Experts

Promotional Banner

Similar Questions

Explore conceptually related problems

If e_(1) and e_(2) be the eccentricities of the hyperbolas 9x^(2) - 16y^(2) = 576 and 9x^(2) - 16y^(2) = 144 respectively, then -

If radii of director circles of x^2/a^2+y^2/b^2=1 and x^2/a^2-y^2/b^2=1 are 2r and r respectively, let e_E and e_H are the eccentricities of ellipse and hyperbola respectively, then

e_(1) and e_(2) are respectively the eccentricites of a hyperbola and its conjugate. Prove that (1)/(e_1^(2))+(1)/(e_2^2) =1

E_(1) and E_(2) are two independent events such that P(E_(1))=0.35 and P(E_(1) cup E_(2))=0.60 , find P(E_(2)) .

If e_1 and e_2 be the eccentricities of a hyperbola and its conjugate, show that 1/(e_1^2)+1/(e_2^2)=1 .

Integrate the functions (e^(2x)-1)/(e^(2x)+1)

If E_(1) ,E_(2),E_(3)…E_(n) be n independent events such that P(Ei)=(1)/(1+i) for 1 le I le n then the chance that none of E_(1),E_(2),E_(3) … E_(n) occur is

Let y=e^(x^(2))" and "y=e^(x^(2))sinx be two given curves. Then the angle between the tangents to the curves at any point of their intersection is-

Let y=e^(x^2) and y=e^(x^2) sinx be two given curves. Then the angle between the tangents to the curves any point of their intersectons is