Thread: Sundials and hyperbolas.

A sundial was designed by Professor John Shepherd. The shadow of the gnomon traces a hyperbola throughout the day. Aluminum rods from the hyperbolas traced on the summer solstice, June 21, and the winter solstice, December 21.

a. One focus of the summer solstice hyperbola is 207 inches above the ground. The vertex of the aluminum branch is 266 inches above the ground. If the x-axis is 355 inches above the ground and the center of the hyperbola is at the origin, write the equation for the summer solstice hyperbola.

b. One focus of the winter solstice hyperbola is 419 inches above the ground. The vertex of the aluminum branch is 387 inches above the ground and the center of the hyperbola is at the origin. If the x-axis is 355 inches above ground, write an equation for the winter solstice hyperbola.