Question:

Find the centre and radius of $x^{2} + y^{2} + 6 y = 0$ .

MHT CET

Updated On: Apr 28, 2025

(A) $(0, 3), 3$
(B) $(- 3, 0), 3$
(C) $(3, 0), 3$
(D) $(0, - 3), 3$

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The Correct Option is D

Solution and Explanation

Explanation:
Given,

x^{2} + y^{2} + 6 y = 0

\Rightarrow x^{2} + y^{2} + 6 y + 9 - 9 = x^{2} + (y + 3)^{2} - 9 = 0

\Rightarrow x^{2} + (y + 3)^{2} = 9

Standard equation of the circle with radius

r

and centre

(h, k)

is given by

(x - h)^{2} + (y - k)^{2} = r^{2}

By comparing, we get

h = 0, k = - 3, r = 3

∴

Centre

= (0, - 3),

Radius

= 3

Hence, the correct option is (D).

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