WAEC Further Mathematics 2023 Paper

Concept:The radius of a circle is found by rewriting its equation in the standard center-radius form: $(x-a)^2+(y-b)^2=r^2$.Explanation:Start with the given equation:$2x^2+2y^2-4x+5y+1=0$.Divide every term by $2$:$x^2+y^2-2x+\frac{5}{2}y+\frac{1}{2}=0$.Move the constant term to the right side:$x^2-2x+y^2+\frac{5}{2}y=-\frac{1}{2}$.Complete the square for $x$:$x^2-2x=(x-1)^2-1$.Complete the square for $y$:$y^2+\frac{5}{2}y=\left(y+\frac{5}{4}\right)^2-\frac{25}{16}$.Substitute these into the equation:$(x-1)^2-1+\left(y+\frac{5}{4}\right)^2-\frac{25}{16}=-\frac{1}{2}$.Simplify:$(x-1)^2+\left(y+\frac{5}{4}\right)^2=\frac{33}{16}$.Therefore, $r^2=\frac{33}{16}$, so:$r=\sqrt{\frac{33}{16}}=\frac{\sqrt{33}}{4}$.The printed option A appears to intend this value; the cube-root form is a typographical error.Answer:$\frac{\sqrt{33}}{4}$