Foci of the Ellipse $25 x^{2} + 9 y^{2} - 150 x - 90 y + 225$ = 0 are

(3,9) (3,1)

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(4,9) (4,1)

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(5,7) (4,7)

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(6,9) (5,1)

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Solution

The correct option is A
(3,9) (3,1)

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

$25 (x^{2} - 6 x) + 9 (y^{2} - 10 y)$ = -225

$25 (x - 3)^{2} + 9 (y - 5)^{2}$ =225 $\Rightarrow$ $\frac{(x - 3)^{2}}{9} + \frac{(y - 5)^{2}}{25}$ = 1

e = $\frac{4}{5}$ , S = (h, k $\pm$ be) = (3,5 $\pm$ 4) = (3,9) and (3,1)

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

Foci of the Ellipse $25 x^{2} + 9 y^{2} - 150 x - 90 y + 225$ = 0 are

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

e

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

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