Home
Class 12
MATHS
If the chord through the points whose ec...

If the chord through the points whose eccentric angles are `theta` and `varphi` on the ellipse `(x^2)/(25)+(y^2)/9=1` passes through a focus, then the value of `tan(theta/2)tan(varphi/2)` is `1/9` (b) `-9` (c) `-1/9` (d) 9

A

`1//9`

B

`-9`

C

`-1//9`

D

9

Text Solution

Verified by Experts

The equation of the line joining `theta and phi` is
`(x)/(5)cos ((theta+phi)/(2))(y)/(3) sin ((theta+phi)/(2))= cos (theta-phi)/(2))`
If it passes through the point (4,0) then
`(4)/(5) cos ((theta+phi)/(2)) = cos (theta-phi)/(2))`
or `(4)/(5)=(cos {(theta-phi)//2})/(cos {(theta+phi)//2)})`
`or (4+5)/(4-5)=(cos {(theta-phi)//2}+cos {(theta+phi)//2})/(cos {(theta-phi)//2}-cos {{(theta+phi)//2}))`
`=(2cos(theta//2)cos (phi//2))/(2 sin (phi//2)sin (phi//2))`
or `tan.( theta)/(2) tan.(phi)/(2)=-(1)/(9)`
If it passes through the point (-4,0) then `tan.(phi)/(2)tan.(theta)/(2)=9`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the chord through the points whose eccentric angles are α and β on the ellipse x^2/a^2+y^2/b^2=1 passes through the focus (ae, 0), then the value of tan(α/2)tan(β/2) is: A. (e+1)/(e−1) B. (e−1)/(e+1) C. (e+1)/(e−2) D. none

If the chord through the points (a sec theta, b tan theta) and (a sec phi, b tan phi) on the hyperbola x^2/a^2 - y^2/b^2 = 1 passes through a focus, prove that tan (theta/2) tan (phi/2) + (e-1)/(e+1) = 0 .

The eccentricity of the ellipse (x^2)/25+(y^2)/9=1 is ,

If costheta=3/4 , then find the value of 9tan^2theta+9 .

If the tangent at the point (2sec theta,3tan theta) to the hyperbola (x^(2))/(4)-(y^(2))/(9)=1 is parallel to 3x-4y+4=0 , then the value of theta , is

Find the equation of tangent at the point theta=(pi)/(3) to the ellipse (x^(2))/(9)+(y^(2))/(4) = 1

The eccentricity of the ellipse (x-1)^(2)/(16)+(y-2)^(2)/(9)=1 is

If the tangent at the point (2sec theta,3tan theta) to the hyperbola (x^(2))/(4)-(y^(2))/(9)=1 is parallel to 3x-y+4=0 , then the value of theta , is

If the chords through point theta and phi on the ellipse x^2/a^2 + y^2/b^2 = 1 . Intersect the major axes at (c,0).Then prove that tan theta/2 tan phi/2 = (c-a)/(c+a) .

If the tangents drawn through the point (1, 2 sqrt(3) to the ellipse x^2/9 + y^2/b^2 = 1 are at right angles, then the value of b is (A) 1 (B) -1 (C) 2 (D) 4