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# 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)

**Solution:**

Since the centre is at (0, 0) and the major axis is on the y-axis,

the equation of the ellipse will be of the form x^{2}/b^{2} + y^{2}/a^{2} = 1, where a is the semi major axis.

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

Hence,

9/b^{2} + 4/a^{2} = 1 ....(1)

1/b^{2} + 36/a^{2} = 1 ....(2)

On solving equations (1) and (2) ,

we obtain a^{2} = 40 and b^{2} = 10

Thus, the equation of the ellipse is x^{2}/10 + y^{2}/40 = 1 or 4x^{2} + y^{2} = 40

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 19

## 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)

**Summary:**

The equation of the ellipse is x^{2}/10 + y^{2}/40 = 1 while the centre is at (0, 0) and the major axis is on the y-axis

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