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 x²/b² + y²/a² = 1, where a is the semi major axis.

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

Hence,

9/b² + 4/a² = 1 ....(1)

1/b² + 36/a² = 1 ....(2)

On solving equations (1) and (2) ,

we obtain a² = 40 and b² = 10

Thus, the equation of the ellipse is x²/10 + y²/40 = 1 or 4x² + y² = 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 x²/10 + y²/40 = 1 while the centre is at (0, 0) and the major axis is on the y-axis