(−14, 34)
(14, 34
(−12, 32)
(−12, −32)
Correct answer is B
2x2 + 2y2 - x - 3y - 41
standard equation of circle
(x-a)2 + (x-b)2 = r2
General form of equation of a circle.
x2 + y2 + 2gx + 2fy + c = 0
a = -g, b = -f., r2 = g2 + f2 - c
the centre of the circle is (a,b)
comparing the equation with the general form of equation of circle.
2x2 + 2y2 - x - 3y - 41
= x2 + y2 + 2gx + 2fy + c
2x2 + 2y2 - x - 3y - 41 = 0
divide through by 2
g = −14 ; 2g = −12
f = −34 ; 2f = −32
a = -g → - −14 ; = 14
b = -f → - (\frac{-3}{4}\) = (\frac{3}{4}\)
therefore the centre is (14, 34)