If the centre,one of the foci,and the semi-ma | vedclass

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(A) Given: Centre $(h, k) = (0, 0)$,Focus $(0, 3)$,and semi-major axis $a = 5$.Since the focus lies on the $y$-axis,the ellipse is vertical with the e

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$\frac{x^2}{16} + \frac{y^2}{25} = 1$

Vedclass · Answer

(A) Given: Centre $(h, k) = (0, 0)$,Focus $(0, 3)$,and semi-major axis $a = 5$.Since the focus lies on the $y$-axis,the ellipse is vertical with the equation $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$.Here,the distance from the centre to the focus is $ae = 3$.Given $a = 5$,we have $5e = 3$,so $e = \frac{3}{5}$.Using the relation $b^2 = a^2(1 - e^2)$,we get $b^2 = 25(1 - (\frac{3}{5})^2) = 25(1 - \frac{9}{25}) = 25 - 9 = 16$.Thus,$b^2 = 16$ and $a^2 = 25$.The equation of the ellipse is $\frac{x^2}{16} + \frac{y^2}{25} = 1$.

If the centre,one of the foci,and the semi-major axis of an ellipse are $(0, 0)$,$(0, 3)$,and $5$ respectively,then its equation is:

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