Pre Calculus Chapter 7 Review
1
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Graph and identify all critical points for the following conic sections.
a) (x+3)2 = -12(y-7)
b) (y+1) 2= 4(x-2)
c)
2.
3.
4.
d)
The towers of the Golden Gate Bridge connecting San Francisco to Marin County are 1280
meters apart and rise 140 meters above the road. The cable between the towers has the shape of
a parabola, and the cable just touches the sides of the road midway between the towers. Find the
height of the cable 200 meters from a tower.
An elliptically shaped garden is surrounded by a wood walkway. The garden is 20 meters long
and 10 meters wide. The walkway is 3 meters wide. Find the equation describing the ellipse that
includes both the garden and the walkway. (Consider the center is at the origin.)
Write the given equation in standard form and identify the conic section
a) y 2  6 y  4 x  17  0
b) 18x – 3x2 - 19 = -8y2 + 32y
c) 4x2+16x+y2-6y-39=0
d) x2 + y2 + 2x - 4y - 11 = 0
5.
Write the equation of a parabola in standard form given the following information
a)
Focus(-6,2); Vertex(-6,-1)
b)
Focus (-3,6); Vertex (7,6)
c)
Focus (3,-6); opens up; contains (9,2)
6.
Write the equation of an ellipse in standard form given:
a)
Foci (19,3) and (-7,3); Length of Major axis = 30
b)
Major axis (-4,4) to (6,4); minor axis (1,1) to (1,7)
c)
Vertex (7,-3) and (3,-3); Foci (6,-3) and (4, -3)
7.
Write the equation of a hyperbola in standard form given:
a)
Vertex (7, 5) and (-5, 5); foci (11, 5) and (-9,5)
b)
Vertex (3,0) and (-3,0); asymptotes
c)
Foci (1,15) and (1,-5); transverse axis length of 16
8.
Find the eccentricity of
9.
a)
b)
An engineer designs a satellite dish with parabolic cross-section. The dish is 15 ft wide at the
opening and the depth is 4 ft. Find the position of the light source (the focus). How far is it
from the deepest part of the dish?
<Answers> ---------------------------------------------------------------------------------------------------1. a) Orientation: vertical; vertex (-3,7); a.o.s. x=-3;focus (-3,4); directrix y = 10 b) horizontal; vertex
(2,-1); a.o.s. y=-1; focus (3,-1); directrix x=1 c) center (2,-3); vertices (8,-3),(-4,-3); foci (8.32,-3),
(-4.32,-3); transverse axis y=-3; conjugate axis x=2; asymptotes
d) center (-1,0);
vertices (-1,7),(-1,-7); co-vertices (4,0),(-6,0); foci (-1,4.9),(-1,-4.9); major axis x=-1; minor axis y=0
2. 66 meters 3.
hyperbola c)
4. a) a) (y  3)2  4( x  2) ; parabola
b)
;
; ellipse d) (x+1)2 + (y-2)2 = 16 ; circle 5. a) (x+6)2= 12(y+1)
b) (y-6)2= -40(x-7)
c) (x-3)2= 4(y+7)
c)
8 . a) 1.52 b) 0.8
7. a)
9. (0, 3.52 ft)
6. a)
b)
b)
c)