Workshop & pre-test problems.

1. Where? Where's the conic?
Generalife by flickr
user ro_lo_be

2. The foci of a hyperbola are F (6, 0) and F (-6, 0), and the difference of
1 2
the focal radii is 4 units. Use the definition of a hyperbola to derive the
equation of this hyperbola.

3. Determine the equation of a parabola defined by the given conditions.
The vertex is V(-1, 3) and the equation of the directrix is x - 2 = 0

4. A rock is kicked off a vertical cliff and falls in a
parabolic path to the water below. The cliff is 40
m high and the rock hits the water 10 m from the
base of the cliff. What is the horizontal distance
of the rock from the cliff face when the rock is at
a height of 30 m above the water?

8. (4) Write the equation
for the graph shown
at right.

11. The cross section of the roof of an indoor tennis court has a semi
elliptical shape. If the roof spans 86 m and has a height of 30 m,
find the height of the roof 20 m from the centre A. HOMEWORK

12. A hyperbola has vertices at (1, -4) and (1, 8). If the asymptotes have
slopes ±2, determine the equation of the hyperbola in standard form.
HOMEWORK

13. The cross section of a HOMEWORK
drainage ditch is parabolic in
shape, as shown in the
diagram at the right. When the
width of the water surface is
10 m, the maximum depth of
the water is 1.5 m. Determine
the width of the water, w, when
the maximum depth is 3 m.