Question

find the equation of ellipse whose major axis is on x-axis and passes through the points (4,3) and (6,2)

Answer 1

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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

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