If the chord through the points whose eccentric angles are $\theta$ and $\phi$ on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ passes through the focus,then the value of $(1 + e) \tan(\frac{\theta}{2}) \tan(\frac{\phi}{2})$ is
- A$e + 1$
- B$e - 1$
- C$1 - e$
- D$0$
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Find the equation of the ellipse with its center at the origin,passing through the points $(-3, 1)$ and $(2, -2)$,given that $a > b$.
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For the ellipse given by $\frac{(x-3)^2}{25}+\frac{(y-2)^2}{16}=1$,match the equations of the lines given in List-$I$ with those on the List-$II$. List-$I$ List-$II$ $(i)$ The equation of the major axis $(p)$ $3x = 34$ $(ii)$ The equation of a directrix $(q)$ $y = 2$ $(iii)$ The equation of a latus rectum $(r)$ $x + y = 9$ $(s)$ $x = 6$ $(t)$ $x = 3$ $(u)$ $3y = 34$
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| $(i)$ The equation of the major axis | $(p)$ $3x = 34$ |
| $(ii)$ The equation of a directrix | $(q)$ $y = 2$ |
| $(iii)$ The equation of a latus rectum | $(r)$ $x + y = 9$ |
| $(s)$ $x = 6$ | |
| $(t)$ $x = 3$ | |
| $(u)$ $3y = 34$ |
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