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

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

Grade:12th pass

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
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Centre = (0, 0), and major axis that passes through the points (3, 2) and (1, 6).

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

(x^2/b^2) + (y^2/a^2) = 1 …. (1)

Here, a is the semi-major axis.

It is given that, the ellipse passes through the points (3, 2) and (1, 6).

Hence, equation (1) becomes

(9/b^2) + (4/a^2) = 1 …(2)

(1/b^2) + (36/a^2) = 1 …(3)

Solving equation (2) and (3), we get

b^2= 10 and a^2= 40

Therefore, the equation of the ellipse becomes: (x^2/10) + (y^2/40) = 1

Thanks

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