Ellipse Test

Result

Ellipse Test - 1

Score
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Rank
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Weekly Quiz Competition

Question 1
1 / -0

The centre of ellipse 4x²+ 9y² + 16x - 18y - 11 = 0 is

A
(2, -1)

B
(-2, 1)

C
(-2, -1)

D
None of these

Solution

The given ellipse is

4x² + 16x + 9y² - 18y = 11

⇒ 4(x² + 4x) + 9(y² - 2y) = 11

⇒ 4(x + 2)² + 9(y - 1)² = 16 + 9 + 11 = 36

⇒ (x + 2)²/36/4 + (y - 1)²/36/9 = 1

Or, (x + 2)²/9 + (y - 1)²/4 = 1

Or, (x + 2)²/3² + (y - 1)²/2² = 1

Let x + 2 = X

So that, when x = -2, X = 0

Similarly, let y - 1 = Y

So that, when y = 1, Y = 0

The equation of the ellipse then becomes X²/3² + Y²/2² = 1

Thus, the centre of the ellipse is (-2, 1).

Hence, answer option (2) is correct.