What is the coordinate of the centre of the circle (5x^{2} + 5y^{2} – 15x + 25y – 3 = 0)?
-
A.
((frac{15}{2}, -frac{25}{2})) -
B.
((frac{3}{2}, -frac{5}{2})) -
C.
((-frac{3}{2}, frac{5}{2})) -
D.
((-frac{15}{2}, frac{25}{2}))
Correct Answer: Option B
Explanation
Equation for a circle: ((x – a)^{2} + (y – b)^{2} = r^{2})
Expanding, we have:
(x^{2} – 2ax + a^{2} + y^{2} – 2by + b^{2} = r^{2})
Given: (5x^{2} + 5y^{2} – 15x + 25y – 3 = 0)
Divide through by 5,
(= x^{2} + y^{2} – 3x + 5y – frac{3}{5} = 0)
Comparing, we have
(- 2a = -3; a = frac{3}{2})
(-2b = 5; b = -frac{5}{2})