Find the coordinates of the centre of the circle (4x^{2} + 4y^{2} – 5x + 3y – 2 = 0).
-
A.
((frac{-5}{4}, frac{3}{4})) -
B.
((frac{3}{8}, -frac{5}{8})) -
C.
((frac{5}{8}, -frac{3}{8})) -
D.
((frac{5}{4}, -frac{3}{4}))
Correct Answer: Option C
Explanation
Equation : ((x – a)^{2} + (y – b)^{2} = r^{2})
Expanding : (x^{2} + y^{2} – 2ax – 2by + a^{2} + b^{2} = r^{2})
Given, (4x^{2} + 4y^{2} – 5x + 3y – 2 = 0)
Divide through by 4 to make the coefficient of (x^{2}) and (y^{2}) to be 1.
(x^{2} + y^{2} – frac{5}{4}x + frac{3}{4}y – frac{1}{2} = 0)
Comparing, (2a = frac{5}{4} implies a = frac{5}{8})
(2b = -frac{3}{4} implies b = -frac{3}{8})
((a, b) = (frac{5}{8}, -frac{5}{8}))