What is the standard equation for a circle centered at (h, k) with radius r?

Given the parabola y = (1/8)x^2, what is the value of p and the coordinates of the focus?

Find the equation of the tangent line to the curve $x^2=8y$ at the point $(4,2)$.

For the hyperbola x^2/9 - y^2/16 = 1, calculate the coordinates of the foci.

A suspension bridge was constructed with two main towers that are $1500$ meters apart. The towers rise $180$ meters above the deck of the bridge. The cable supporting the deck between the towers forms a parabolic shape. By placing the origin at the midpoint of the bridge deck between the towers, find the quadratic equation that models the shape of the cable. Then, calculate the height of the cable above the deck at a point $600$ meters from the center of the bridge.