The equation of the ellipse whose one of the vertices is $(0,7)$ and the corresponding directrix is $y = 12$, is
The equation of the ellipse whose one of the vertices is $(0,7)$ and the corresponding directrix is $y = 12$, is
- A
$95{x^2} + 144{y^2} = 4655$
- B
$144{x^2} + 95{y^2} = 4655$
- C
$95{x^2} + 144{y^2} = 13680$
- D
None of these
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The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1$, is .............. $\mathrm{sq. \,units}$
The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1$, is .............. $\mathrm{sq. \,units}$
- [IIT 2003]
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Eccentricity of the conic $16{x^2} + 7{y^2} = 112$ is
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Let $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right), y_1<0, y_2<0$, be the end points of the latus rectum of the ellipse $x^2+4 y^2=4$. The equations of parabolas with latus rectum $P Q$ are
$(A)$ $x^2+2 \sqrt{3} y=3+\sqrt{3}$
$(B)$ $x^2-2 \sqrt{3} y=3+\sqrt{3}$
$(C)$ $x^2+2 \sqrt{3} y=3-\sqrt{3}$
$(D)$ $x^2-2 \sqrt{3} y=3-\sqrt{3}$
Let $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right), y_1<0, y_2<0$, be the end points of the latus rectum of the ellipse $x^2+4 y^2=4$. The equations of parabolas with latus rectum $P Q$ are
$(A)$ $x^2+2 \sqrt{3} y=3+\sqrt{3}$
$(B)$ $x^2-2 \sqrt{3} y=3+\sqrt{3}$
$(C)$ $x^2+2 \sqrt{3} y=3-\sqrt{3}$
$(D)$ $x^2-2 \sqrt{3} y=3-\sqrt{3}$
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