Q. 19

In each of the following, find the equation for the ellipse that satisfies the given conditions:

Centre at (0,0), major axis on the y-axis and passes through the points (3, 2) and (1,6).

Answer :

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


=1 ………………….(1)


Where, a is the semi - major axis


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


=1 …………………… (2)


=1……………………… (3)


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


Thus, the equation of the ellipse is = 1 or 4x2 + y 2 = 40.

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