MB31 –Review Sheet 3 Answers

MB31 –Review Sheet 3 Answers
Name KEY
1. In circle O, chords AB and CD intersect at E. If AE = 4, EB = 12, and ED = 16.
Find the measure of CE .
When two chords are drawn in a circle,
the product of the segments of one chord is equal
to the product of the segments of the other chord.
AE • EB = CE • ED
4• 12= x • 16
48 = 16x
3 = x
Therefore CE = 3.
2. Tangent PA and secant PBC are drawn to circle O from point P. If PB = 4, and BC = 5,
find the measure of PA .
When a tangent and a secant are drawn to a circle
from the same external point, the product of the secant
and it’s external segment is equal to the tangent squared.
PC • PB = ( PA)
(4 + 5) • 4 = x
2
2
36 = x
6 = x
2
Therefore PA = 6.
3. Secants PBC and PDE are drawn to circle O from point P. If PBC = 20, PB = 5, and DE = 21,
find the measure of PDE .
When two secants are drawn to a circle from the same
external point, the product of one secant and it’s
external segment is equal to the product of the other
secant and it’s external segment.
PC • PB = PE • PD
20• 5 = xx ( + 21)
2
100 = + 21
x
x
x
2
+ 21x− 100 = 0
( x+ 25)( x− 4) = 0
x=− 25 x=
4
Reject
Since x = 4 the measure of PDE = x + 21 = 4 + 21 = 25
4. Identify each graph as of one of the following: line, circle, ellipse, parabola, hyperbola, equilateral hyperbola
a)
2 2
2x
= 16− y Ellipse
h)
2
4x
y 25
+ = Parabola
b)
2 2 2
x + 5= 21−2y − x Circle
i)
y
2
= ( x− 3) Parabola
c)
d)
e)
x
x
− 4y
= 36 Hyperbola
2 2
2
− 4y
= 36 Parabola
2 2
2x
4y
36
+ = Ellipse
f) xy = 12
Equilateral Hyperbola
g) x+ y = 12
Line
j)
k)
l)
m)
5
x = Equilateral Hyperbola
y
2 2
2y
= 6− x Ellipse
2 2
6x
= 12+ 2y
Hyperbola
2 2
36 − x = y Circle
n) 4xy = − 16 Equilateral Hyperbola

5. Sketch the graph:
a)
2 2
( x 5) ( y 1) 4
+ + − = b)
2 2
( x+
2) y
+ = 1
c) xy = 10
9 36
Circle with center at (-5, 1) Ellipse with center at (-2, 0) Equilateral hyperbola
includes points: includes points: in Quadrants I and III
(-7, 1), (-3, 1), (-5, 3), (-5, -1) (-5, 0), (1, 0), (-2, 6), (-2, -6)
c)
2 2
x y
− = 1
d)
36 16
y = −
2
2x
6
Hyperbola
Parabola
with x-intercepts at x =± 6
opens upward with y − int =− 6
6. An ellipse has its center at (-1, 2). Its minor axis is vertical and has a length of 8. Its major axis is horizontal
and has a length of 10. Write an equation for this ellipse.
2 2
( x−h) ( y−k)
+ = 1
2 2
a b
2 2
( x+ 1) ( y−2)
+ = 1
25 16
Since the length of the axes are given, you need to
divide them by two first and then square them to find
the denominators.
7. Because Kelly’s coach believes that every
player should get an equal opportunity to play, she
varies the playing time so that it is inversely
proportional to the number of players who show up
for a game. When the whole team of 16 players
attends, each player has 18 minutes of play time.
How many players must be absent for Kelly to play
for 24 minutes
a) 12 b) 8 c) 6 d) 4
(18)(16) = 24x
288 = 24x
x = 12
Since 12 players must be
present, 4 players must
be absent.
8. When David drives to Melissa’s college to visit
her, his travel time varies inversely as his speed.
If he drives at 56 miles/hour, he arrives in 3 hours.
How many minutes would he save if he traveled at
60 miles/hour
a) 80 b) 40 c) 28 d) 12
(56)(3) = 60x
168 = 60x
x = 2.8 hours
He would save 0.2 hours,
which is 12 minutes.

9. If p varies inversely as q, find the missing
value in the table:
p 40 30 20
q 9 x 18
a) 4.5 b) 12 c) 15 d) 16
(40)(9) = 30x
360 = 30x
x = 12
10. If a varies directly as b, and a = 28 when
b = 8, what is a when b = 14
a) 49 b) 16 c) 3.5 d) 98
28 a
=
8 14
8a = 392
a = 49
11. Each of the graphs is a transformation of the graph of
y
2
= x . Find an equation for each of the functions.
y =− ( x+
4)
2
y = + +
2
( x 1) 2
y = − − +
2
( x 3) 2
12. Write an equation of the graph
y
2
= x after the following transformation:
a) Shifted 2 units to the left and 4 units up.
b) Reflected in the x-axis, shifted 5 units down and 1 unit to the right.
y = + +
2
( x 2) 4
y =− − −
2
( x 1) 5