Find the equation for the ellipse that satisfies the given conditionsCentre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Asked by Pragya Singh | 11 months ago |  77

1 Answer

Solution :-

Since the centre is at (0, 0) and the major axis is on the y-axis, the equation of the ellipse will be of the form

 \( \dfrac{x^2}{a^2}\) +\( \dfrac{y^2}{b^2}\) = 1.............(1)

Where, a is the semi-major axis

The ellipse passes through points (3, 2) and (1, 6). Hence

\( \dfrac{9}{b^2}+\dfrac{4}{a^2}\)…. (2)

\( \dfrac{1}{b^2}+\dfrac{36}{a^2}\) ..........(3)

On solving equations (2) and (3), we obtain b2= 10 and a2= 40.

Thus, the equation of the ellipse is \( \dfrac{x^2}{10}+ \dfrac{y^2}{40}=1\)

or 4x2 + y2 = 40

Answered by Abhisek | 11 months ago

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