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Question
Select the correct option from the given alternatives:
Centre of the ellipse 9x2 + 5y2 − 36x − 50y − 164 = 0 is at
Options
(2, 5)
(1, −2)
(−2, 1)
(0, 0)
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Solution
(2, 5)
Explanation:
The given equation can be written as:
(9x2 – 36x) + (5y2 – 50y) = 164
∴ 9(x2 – 4x + 4) + 5(y2 – 10y + 25) = 164 + 36 + 125
∴ 9(x – 2)2 + 5(y – 5)2 = 325
∴ `("x" - 2)^2/((325/9)) + ("y" - 5)^2/65` = 1
This is of the form `"X"^2/"a"^2 + "Y"^2/"b"^2` = 1, where X = x – 2, Y = y – 5.
∴ centre of the ellipse is given by
X = x – 2 = 0 and Y = y – 5 = 0
∴ x = 2, y = 5
∴ centre = (2, 5)
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