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Question
The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–3, 1) and (2, –2) is ______.
Options
5x2 + 3y2 = 32
3x2 + 5y2 = 32
5x2 – 3y2 = 32
3x2 + 5y2 + 32 = 0
Solution
The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–3, 1) and (2, –2) is 3x2 + 5y2 = 32.
Explanation:
Let `x^2/a^2 + y^2/b^2` = 1 be the equation of the ellipse.
Then according to the given conditions
We have `9/a^2 + 1/b^2` = 1 and `1/a^2 + 1/b^2 - 1/4`
Which gives `a^2 = 32/3` and `b^2 = 32/5`.
Hence, required equation of ellipse is 3x2 + 5y2 = 32.
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