The equation of a circle is (3x^{2} + 3y^{2} + 24x – 12y = 15). Find its radius.
-
A.
2 -
B.
3 -
C.
4 -
D.
5
Correct Answer: Option D
Explanation
The equation of a circle is given as: ((x – a)^{2} + (y – b)^{2} = r^{2})
Expanding, we have: (x^{2} + y^{2} – 2ax – 2by + a^{2} + b^{2} = r^{2})
(implies x^{2} + y^{2} – 2ax – 2by = r^{2} – a^{2} – b^{2})
Comparing with the given equation: (3x^{2} + 3y^{2} + 24x – 12y = 15)
Making the coefficients of (x^{2}) and (y^{2}) = 1, we have
(x^{2} + y^{2} + 8x – 4y = 5)
(2a = -8 implies a = -4)
(2b = 4 implies b = 2)
(r^{2} – a^{2} – b^{2} = 5 implies r^{2} = 5 + (-4)^{2} + (2)^{2} = 5 + 16 + 4 = 25)
(therefore r = 5)