Chapter 7 Practice Test With Answers - Montville Township Public Schools Page 4
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1
2
3
4
5
6
7
8
9=
Using the values of h, k, a, and b, the equation for
Practice Test - Chapter 7
the hyperbola is
–
= 1.
Write an equation for each conic in the xy –
10.
+
= 1, θ =
plane for the given equation in x′y′ form and the
given value of θ.
SOLUTION:
2
9.
7(x′ – 3) = (y′ )
, θ = 60º
+
= 1, θ =
SOLUTION:
Use the rotation formulas for x′ and y′ to find the
2
equation of the rotated conic in the xy–plane.
7(x′ – 3) = (y′ )
, θ =
x′ = x cos θ + y sin θ
Use the rotation formulas for x′ and y′ to find the
x′ =
x +
y
equation of the rotated conic in the xy–plane.
x′ = x cos θ + y sin θ
y′ = y cos θ − x sin θ
x′ =
x +
y
y′ =
y −
x
y′ = y cos θ − x sin θ
Substitute these values into the original equation.
y′ =
y −
x
Substitute these values into the original equation.
Graph the hyperbola given by each equation.
11.
–
= 1
10.
+
= 1, θ =
SOLUTION:
SOLUTION:
The equation is in standard form, with h = 0 and k =
2
2
4. Because a
= 64 and b
= 25, a = 8 and b = 5.
+
= 1, θ =
The values of a and b can be used to find c.
2
2
2
c
= a
+ b
Use the rotation formulas for x′ and y′ to find the
2
c
= 64 + 25
equation of the rotated conic in the xy–plane.
c =
or about 9.43
x′ = x cos θ + y sin θ
Use h, k, a, b, and c to determine the characteristics
x′ =
x +
y
of the hyperbola.
orientation: In the standard form of the equation, the
y′ = y cos θ − x sin θ
y–term is being subtracted. Therefore, the
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Page 4
y′ =
y −
x
orientation of the hyperbola is horizontal.
center: (h, k) = (0, 4)
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