An ellipse having foci at (3, 3) and (- 4, 4) and passing through origin has eccentricity equ

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10-2. Parabola, Ellipse, Hyperbola

normal

An ellipse having foci at $(3, 3) $ and $(- 4, 4)$ and passing through the origin has eccentricity equal to

$\frac{3}{7}\,$

$\frac{2}{7}\,$

$\frac{5}{7}\,$

$\frac{3}{5}\,$

Solution

$PS_1 + PS_2 = 2a$
$3\sqrt 2 \, + 4\sqrt 2 \,\, = \,2a$
$\therefore \,2a\, = \,7\sqrt 2 \,$
Also $2ae = S_1S_2 = \sqrt {1 + 49} \, = \,5\sqrt 2 \,$
$\therefore \,\frac{{2ae}}{{2a}}\,\, = \,\,\frac{{5\sqrt 2 }}{{7\sqrt 2 }}\,\, = \,\frac{5}{7}\, = e $

Standard 11

Mathematics

If the co-ordinates of two points $A$ and $B$ are $(\sqrt{7}, 0)$ and $(-\sqrt{7}, 0)$ respectively and $P$ is any point on the conic, $9 x^{2}+16 y^{2}=144,$ then $PA + PB$ is equal to

medium

(JEE MAIN-2020)

The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points $(4,-1)$ and $(-2, 2)$ is

hard

(JEE MAIN-2017)

Let $P$ be an arbitrary point on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ $a > b > 0$. Suppose $F_1$ and $F_2$ are the foci of the ellipse. The locus of the centroid of the $\Delta P F_1 F_2$ as $P$ moves on the ellipse is

normal

(KVPY-2010)

For the ellipse $25{x^2} + 9{y^2} – 150x – 90y + 225 = 0$ the eccentricity $e = $