Question

4. For the equation of the ellipse, find the coordinates of the center, foci and vertices.
(x-4)^2/16+(y+6)^2/9=1

6. Automobile headlights contain parabolic reflectors, which work on the principle that light placed at
the focus of a parabola will reflect off the mirror-like surface in lines parallel to the axis of symmetry.
Suppose a bulb is placed at the focus of a headlight’s reflector, which is 2 inches from the vertex.
If the depth of the headlight is to be 4 inches, what should the diameter of the headlight be at its
opening?

Answer 1

(x-4)^2/16+(y+6)^2/9=1
center: (4,-6)
a=4 and b=3, so c = √7
vertices are at (4±4,-6)
covertices are at (4,-6±3)
foci are at (4±√7,-6)

Answer 2

The diameter of the headlight at its opening should be 8 inches.