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Question

For the ellipse 25x2+9y2-150x-90y+225=0, the eccentricity is equal to


A

25

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B

35

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C

1524

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D

45

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Solution

The correct option is D

45


Explanation for the correct option:

Equation for an ellipse:

(x-h)2a2+(y-k)2b2=1...(A)

Eccentricity of an ellipse.

25x2+9y2-150x-90y+225=025(x2-6x)+9(y2-10y)+225=025(x2-6x+9)+9(y2-10y+25)=225(x-3)29+(y-5)225=1...(B)Compareeqn(A)&(B)Here,a=3,b=5Now,e=1-a2b2e=1-925e=45

Hence, the correct option is (D)


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