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: 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
\(- 2a = -3; a = \frac{3}{2}\)
\(-2b = 5; b = -\frac{5}{2}\)
