WAEC Further Mathematics 2016 Paper

Given the endpoints of the diameter |EF|, the midpoint is the centre of the circle

= $(\frac{-2+3}{2}, \frac{-1+2}{2}) = (\frac{1}{2}, \frac{1}{2})$

The radius is the distance from the centre to any point on the circle. Using $(\frac{1}{2}, \frac{1}{2})$ and $(3, 2)$;

$r^{2} = (3 - \frac{1}{2})^{2} + (2 - \frac{1}{2})^{2} = \frac{25}{4} + \frac{9}{4}$

$r^{2} = \frac{34}{4}$

The equation of a circle is given as:

$(x - a)^{2} + (y - b)^{2} = r^{2}$, (a, b) as the centre of the circle.

$= (x - \frac{1}{2})^{2} + (y - \frac{1}{2})^{2} = \frac{34}{4}$

$x^{2} - x + \frac{1}{4} + y^{2} - y + \frac{1}{4} = \frac{17}{2}$

= $x^{2} - y^{2} - x - y - 8 = 0$