If the chord through the point whose eccentric angles are θ φ on the ellipse, ( x 2 / a 2)+( y 2 / b 2)=1 passes through the focus, then the value of (1+ e ) tan (θ / 2) tan (φ / 2) is

Question

If the chord through the point whose eccentric angles are θ φ on the ellipse, ( x 2 / a 2)+( y 2 / b 2)=1 passes through the focus, then the value of (1+ e ) tan (θ / 2) tan (φ / 2) is (A) e +1 (B) e -1 (C) 1- e (D) 0

Tardigrade Admin · Accepted Answer

Chord: ( x / a ) cos ((θ+φ/2))+( y / b ) sin ((θ+φ/2))= cos ((θ-φ/2))

Q. If the chord through the point whose eccentric angles are $θ & ϕ$ on the ellipse, $(x^{2} / a^{2}) + (y^{2} / b^{2}) = 1$ passes through the focus, then the value of $(1 + e) tan (θ /2) tan (ϕ /2)$ is

$e + 1$

$e - 1$

$1 - e$

0

Chord: $\frac{x}{a} cos (\frac{θ + ϕ}{2}) + \frac{y}{b} sin (\frac{θ + ϕ}{2}) = cos (\frac{θ - ϕ}{2})$

Q. If the chord through the point whose eccentric angles are θ&ϕ on the ellipse, (x2/a2)+(y2/b2)=1 passes through the focus, then the value of (1+e)tan(θ/2)tan(ϕ/2) is

e+1

e−1

1−e

0

Chord: ax​cos(2θ+ϕ​)+by​sin(2θ+ϕ​)=cos(2θ−ϕ​)

Q. If the chord through the point whose eccentric angles are $θ & ϕ$ on the ellipse, $(x^{2} / a^{2}) + (y^{2} / b^{2}) = 1$ passes through the focus, then the value of $(1 + e) tan (θ /2) tan (ϕ /2)$ is

$e + 1$

$e - 1$

$1 - e$

Chord: $\frac{x}{a} cos (\frac{θ + ϕ}{2}) + \frac{y}{b} sin (\frac{θ + ϕ}{2}) = cos (\frac{θ - ϕ}{2})$