Home
Class 12
MATHS
The eccentric angle of a point on the el...

The eccentric angle of a point on the ellipse `(x^2)/4+(y^2)/3=1` at a distance of 5/4 units from the focus on the positive x-axis is `cos^(-1)(3/4)` (b) `pi-cos^(-1)(3/4)` `pi+cos^(-1)(3/4)` (d) none of these

A

`cos^(-1)(3//4)`

B

`cos^(-1)(4//5)`

C

`cos^(-1)(3//5)`

D

none of these

Text Solution

Verified by Experts

Any point on the ellipse is `(2cos theta, sqrt(3) sin theta)`
The focus on the positive x-axis is (1,0)
Given that
`(2 cos theta-1)^(2)+3sin^(2)theta=(25)/(16)`
or `cos theta=(3)/(4)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The eccentric angle in the first quadrant of a point on the ellipse (x^(2))/(10) +(y^(2))/(8) = 1 at a distance 3 units from the centre of the ellipse is _

The distance of a point on the ellipse (x^2)/6+(y^2)/2=1 from the center is 2. Then the eccentric angle of the point is pi/4 (b) (3pi)/4 (c) (5pi)/6 (d) pi/6

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

The angle between the tangents to the curves y=x^2a n dx=y^2a t(1,1) is cos^(-1)(4/5) (b) sin^(-1)(3/5) tan^(-1)(3/4) (d) tan^(-1)(1/3)

tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0, is equal to x (b) 2x (c) 2/x (d) none of these

The angle formed by the positive y - axis and the tangent to y=x^2+4x-17 at (5/2,-3/4) is: (a) tan^(-1)(9) (b) pi/2-tan^(-1)(9) pi/2+tan^(-1)(9) (d) none of these

2tan^(-1)(-2) is equal to (a) -cos^(-1)((-3)/5) (b) -pi+cos^(-1)3/5 (c) -pi/2+tan^(-1)(-3/4) (d) -pi+cot^(-1)(-3/4)

cos^(-1)("cos"(2cot^(-1)(sqrt(2)-1))) is equal to (a) sqrt(2)-1 (b) pi/4 (c) (3pi)/4 (d) none of these

sin^(-1)x-sin ^(-1)y=(pi)/(3) and cos^(-1) x+ cos ^(-1) y=(2pi)/(3)

The value of the integral int_(-(3pi)/4)^((5pi)/4)((sinx+cosx)/(e^(x-pi/4)+1))dx (A) 0 (B) 1 (C) 2 (D) none of these