For the ellipse 25 x^2 + 9 y^2 - 150x - 90y + 225 = 0 the eccentr… - Vidyadip

MCQ

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

A
$2\over5$
B
$3\over5$
✓
$4\over5$
D
$1\over5$

✓

Answer

Correct option: C.

$4\over5$

c
(c) Given equation of ellipse is ,

$25{x^2} + 9{y^2} - 150x - 90y + 225 = 0$

$ \Rightarrow $$25\,{(x - 3)^2} + 9{(y - 5)^2} = 225$

$ \Rightarrow $$\frac{{{{(x - 3)}^2}}}{9} + \frac{{{{(y - 5)}^2}}}{{25}}$ = 1. Here $b > a$

$\therefore $ Eccentricity $e = \sqrt {1 - \frac{{{a^2}}}{{{b^2}}}} = \sqrt {1 - \frac{9}{{25}}} $

$ = \sqrt {\frac{{16}}{{25}}} = \frac{4}{5}$.

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