AHSME 1969 Problem 26

A parabolic arch has a height of $16$ inches and a span of $40$ inches. The height, in inches, of the arch at the point $5$ inches from the center $M$ is: $\text{(A) } 1 \text{(B) } 15 \text{(C) } 15\tfrac{1}{3} \text{(D) } 15\tfrac{1}{2} \text{(E) } 15\tfrac{3}{4}$