I would be gratefull if anybody can help me on this problem.
Plot the curve y = 1/2X ^ 2 and decide the equation for the
normal lines which can be drawn to the curve from the point (0,9).
Consider a line $\displaystyle l$ from $\displaystyle (0,9)$ to a point on the curve $\displaystyle (a, \frac{1}{2}a^2)$.
Find the slope.of the tangent line $\displaystyle l'$ to the curve at $\displaystyle x=a$.
Check when $\displaystyle l$ is perpendicular to $\displaystyle l'$ using slope.