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For the circle $x 2 + y 2 + 3 x + 3 y = 0$ , Which of the following is true?

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Centre lies on X-axis

Centre lies on Y-axis

Centre is at origin

Circle passes through origin

answer is D.

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Detailed Solution

Let the circle be

x 2 + y 2 + 3 x + 3 y = 0

. The general form of the circle is

(x − α) 2 + (y − β) 2 = r 2

.
Rewriting the given equation in the form of general equation, and we have

x + 32 2 + y + 32 2 = 92

Equating the above equation with the general equation, we get
Centre is

O = − 32, − 32

, and Radius is

32

units.
We can say that the centre doesn’t pass through the X and Y axes, and it is not the origin.
Let’s see the circle passes through the origin or not, by substituting

x = y = 0

x 2 + y 2 + 3 x + 3 y = 0 + 0 + 3 (0) + 3 (0) = 0

Therefore, the point

(0, 0)

satisfies the circle and it passes through the origin.
Hence, the correct option is 4.

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