Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4, 3) and (6, 2)

Solution:

Since the center is at (0, 0) and the major axis is on the x-axis,

the equation of the ellipse will be of the form x²/a² + y²/b² = 1, where a is the semi major axis.

The ellipse passes through points (4, 3) and (6, 2).

Hence,

On substituting the value of x and y as (4, 3), we get

16/b² + 9/a² = 1 ....(1)

On substituting the value of x and y as (6, 2), we get

36/b² + 4/a² = 1 ....(2)

On solving equations (1) and (2) ,

we obtain a² = 52

and b² = 13

Thus, the equation of the ellipse is x²/52 + y²/13 = 1 or x² + 4y² = 52

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NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.3 Question 20

Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4, 3) and (6, 2).

Summary:

The equation of the ellipse is x²/52 + y²/13 = 1 while the center is at (0, 0) and the major axis is on the x-axis