WAEC 2022 · Paper 1 · Q9

If $x^2 + y^2 - 2x - 6y + 5 = 0$ , evaluate $\dfrac{dy}{dx}$ when $x = 3$ and $y = 2$ .

Worked solution (try it first)

Differentiate each term with respect to $x$ , using the chain rule on the $y$ terms: $2x + 2y\dfrac{dy}{dx} - 2 - 6\dfrac{dy}{dx} = 0$ .
Collect the $\dfrac{dy}{dx}$ terms: $(2y - 6)\dfrac{dy}{dx} = 2 - 2x$ , so $\dfrac{dy}{dx} = \dfrac{2 - 2x}{2y - 6}$ .
Put in $x = 3$ , $y = 2$ : $\dfrac{2 - 6}{4 - 6} = \dfrac{-4}{-2} = 2$ , option B.