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).

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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