# 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 x^{2}/a^{2} + y^{2}/b^{2} = 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/b^{2} + 9/a^{2} = 1 ....(1)

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

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

On solving equations (1) and (2) ,

we obtain a^{2} = 52

and b^{2} = 13

Thus, the equation of the ellipse is x^{2}/52 + y^{2}/13 = 1 or x^{2} + 4y^{2} = 52

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 x^{2}/52 + y^{2}/13 = 1 while the center is at (0, 0) and the major axis is on the x-axis

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