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).

Explanation

To find the equation of the ellipse that satisfies the given conditions, we will follow these steps:

### Step 1: Write the standard form of the ellipse equation
Since the center is at (0, 0) and the major axis is along the y-axis, the standard form of the ellipse equation is:
\[ \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1 \]
where \(a^2\) is the square of the semi-major axis and \(b^2\) is the square of the semi-minor axis.
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