Precalculus
HW#85 DUE TUESDAY 4/28 worth 6 points
Name:
Leave answers EXACT unless otherwise stated.
1. Use the equation
( x  4) 2 ( y  2) 2

 1 to draw an accurate graph.
16
4
Name the foci : _______________________________
2. Use the equation
( y  2)2 ( x  1)2

 1 to draw an accurate graph.
9
27
(Include the foci)
Write the asymptotes : _______________________
3. Use the equation x2  6x  2 y  5  2 to find the missing information and draw an accurate graph.
a) Which conic section does this equation represent? ____________
b) vertex: ____________
c) focus: _____________
d) directrix: ________________
e) 2 points on the Latus Rectum: _____________________
Write an equation for each conic described below and any other listed information. I recommend making a sketch.
4. Parabola: focus (-2, -8): vertex (2, -8)
5. Ellipse: center at (-1,2); a focus at (-1,8); a vertex at
(-1,10)
Equation: __________________________
Equation: __________________________
Directrix: __________________________
Coordinates of co- vertices: ___________________
6. Hyperbola with asymptotes at y  3  
2 7
 x  4  and one vertex at (-1, 3).
3
Equation: _________________________
Write in standard form and identify the name of the conic.
7. 16 x 2  4 y 2  64 x  8 y  196  0
Equation ______________________
Name ________________________
For the application problems you may round your answers to the hundredth place.
8. A new bridge is being built over the Petaluma River. The bridge must have a span of 200 feet and a height of 40 feet.
If the bridge has a semi-elliptical arch, find the height of the arch 40 feet from the center.
9. Consider the following diagram of a bridge: AB is 70 m and is the longest vertical support of a bridge which contains a
parabolic arch. The vertical supports are 10 meters apart. The arch meets the vertical end supports 6 meters above the
road.
a) If axis are drawn on the diagram of the bridge, with x-axis the road and y-axis on AB, find the equation of the
parabolic arch.
b) Find the length of the vertical support that is 30 meters from the center.
10. A satellite dish shaped like a paraboloid of revolution is receiving TV signals. If the dish has a diameter of 4 feet and
a depth of 2.5 feet, where is the receiver?
11. A building has an elliptical ceiling. Josh realizes that if he stands 25 feet from the center of the building that he can
hear what people are saying at the other side of the building. Assuming Josh is standing under one focus, and the
building is 60 feet wide, how tall is the elliptical ceiling?