Precalculus Practice Test 9.19.3 - South Minneapolis High School Page 7
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9Precalculus Practice Test 9.1-9.3
12. Find the center and foci of the hyperbola.
2
2
y
+ 6
x
+ 3
1
49
32
Because the y term is positive, the transverse axis of this hyperbola is vertical. The standard
y k
2
x h
2
1
equation of such a hyperbola is
. Comparing terms, we can see that
2
2
a
b
32 4 2
the center of this hyperbola is (‐3,‐6), a is 7, and b is equal to
.
The foci are located c units from the center, so we need to solve for c. In a hyperbola,
a
b
2
2
2
c
2
7
2
2
c
32
49 32
81
c 9
Since the transverse axis is vertical, we need to move 9 units up from the center and 9 units
down. The center is (‐3,‐6) and the foci are (‐3,‐15) and (‐3,3).
13. Classify the graph of the equation below as a circle, a parabola, an ellipse, or a
hyperbola.
2
2
3
y
11
x
y
67 0
2
2
Looking at this equation, we really need only to focus on the coefficients of x
and y
. The
2
2
terms in question are
11x
and
3y
. The coefficients are different, but both are positive. This
is the equation of an ellipse.
Page 7
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