Mathematics - Application of Derivative Question with Solution | TestHub

The point P(x0, y0) on the curve nearest to the line is where the normal at P is perpendicular to the line x + y = 4, whose slope is -1, so the normal at P has slope 1. For y^2 = 4(x - 10), differentiating gives 2y y' = 4, so the tangent slope at P is 2/y0 and the normal slope is -y0/2. Setting -y0/2 = 1 gives y0 = -2, and then x0 = 10 + y0^2/4 = 11. The nearest point is P(11, -2). Answer: option C.