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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
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
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