#62. Civil engineers often design road surfaces with parabolic cross sections to provide water drainage. Assume a road surface on level ground is 32 feet wide and is 0.4 foot higher at its center point than at its edges. (a.) Derive in standard form the equation of that (b.) surface's parabola, assuming the parabola's vertex is at the origin of your coordinate system. Use that equation to calculate the distance from the road's centerline to the point at which the road surface is 0.1 foot lower than at the centerline.

3. Reason Jupiter's gravity changes a spacecraft's path to a hyperbola as it approaches. The focus of the hyperbola nearest the spacecraft's path is the center of Jupiter. The diameter of the planet is 139,822 km. Suppose the path of an approaching spacecraft has an equation with a = 80,000 km and c= 170,000 Km. Assuming the transverse axis.js horizontal, write the equation that models the path of the spacecraft as it approaches Jupiter. What is the distance from the spacecraft to the planet at the vertex of the hyperbola?

Classify the following parabola as horizontal and vertical, indicate where they open.

1. Find the equation of the parabola with its axis parallel to the y-axis, vertex at (-3, 2) and passing through the point (1, 0). State the focus and equation of the directrix line. Hence, sketch the parabola.