Equation of an ellipse with centre at the origin passing through (5,0) and having eccentricity 2/3 is.

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16x2+5y2 =25

9x2+5y2 =25

5x2+9y2 =25

5x2+16y2 =25

answer is C.

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Detailed Solution

Let the equation of the ellipse be x2a2+y2b2=1.It passes through (5,0)⇒a2=25b2=a21−e2⇒b2=251−49=1259Hence the required equation of the ellipse is 5x2+9y2 =25

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