(1) A hyperbolic reflector for a radiotelescope has the equation :
y^2/900-x^2/225=1.
If the reflector has a diameter of 20 feet, how deep is it (in feet)?
(2)A nuclear cooling tower is in the shape of a hyperboloid(that is, a hyperbola rotated around its conjugate axis). The equation of the hyperbola is :
x^2/5625-y^2/10000=1
If the center of the tower (the narrowest part) is 100 feet above the ground, what is the diameter (in feet) of the circular base?
(3) A semi-elliptical arch in a bridge over a river has a span of 40 feet and a clearance of 12 feet above the water in the middle of the bridge. How much distance (in feet) above the water is there 5 feet from the banks?
PLLLLEEEASSSE help set these up for me.
Place the origin on the surface of the water and in the middle of the bridge. The semi-axes are a = 20' and b = 12. Therefore the equation of the ellipse is:
A point 5' from the bank is 15' away from the origin. Plug in x = 15 into the equation above and solve for y (The negative value is for divers only)
I've got