Answers LAUSD-Algebra II B Prescriptive - SummerEquations of Hyperbolas

Unit Test Answers

25 verified answers

Which equation represents the circle described?The radius is 2 units. The center is the same as the center of a circle whose equation is x2 + y2 – 8x – 6y + 24 = 0.

(x + 4)2 + (y + 3)2 = 2

(x – 4)2 + (y – 3)2 = 2

(x – 4)2 + (y – 3)2 = 2²

(x + 4)2 + (y + 3)2 = 2²

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A parabola can be represented by the equation x2 = 2y.

focus: (0,8); directrix: y = –8

focus: ; directrix: y =

focus: (8,0); directrix: x = –8

focus: ; directrix: x =

The center of a hyperbola is located at the origin. One focus is located at (0, 20), and its associated directrix is represented by the line y = . What is the equation of the hyperbola?

= 1

= 1

= 1

A parabola and its focus are shown on the graph. The vertex of the parabola is at (0,0).

y = 3

y = –3

x = 3

x = –3

An ellipse has vertices along the major axis at (0, 1) and (0, −9). The foci of the ellipse are located at (0, −1) and (0, −7). The equation of the ellipse is in the form below.

a = 10

b = 4

h = 3

k = 0

Question text not available

points G and H ✓ Correct

points J and K

points L and N

points M and N

Which equation represents a hyperbola with a center at (0, 0), a vertex at (−48, 0), and a focus at (50, 0)?

= 1

A point is on a circle if the distance from the center of the circle to the point is equal to the

area.

circumference.

radius.

diameter.

What are the foci of the hyperbola whose equation is = 1?

(−6, 2) and (14, 2)

(−4, 2) and (12, 2)

(4,−8) and (4, 12)

(4,−6) and (4, 10)

Question text not available

(1,−2)

(1, 1)

(1, 3)

(1, 6)

The graph of a hyperbola is shown.

(0, −4)

(−3, 0)

(0, 0)

(0, 5)

A general formula for a parabola is x2=4py.What is the value of p in the equation x2=12y?

p=3

p=4

p=6

p=12

What are the vertices of the hyperbola whose equation is = 1?

(−13, 8) and (−1, 8)

(−12, 8) and (−2, 8)

(−7, 2) and (−7, 14)

(−7, 3) and (−7, 13)

Question text not available

x = −4.25 and x = 8.25

x = −3.25 and x = 9.25 ✓ Correct

y = −4.25 and y = 8.25

y = −3.25 and y = 9.25

The graph of an ellipse is shown.

Option

1.82.83.84.8

1.8

2.8

3.8

4.8

What is the radius of a circle whose equation is (x + 5)2 + (y – 3)2 = 42?

2 units

4 units

8 units

16 units

A parabola with a vertex at (0,0) has a directrix that crosses the negative part of the y-axis.

x2 = –4y

x2 = 4y

y2 = 4x

y2 = –4x

Which graph represents the hyperbola = 1?

Option

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units.The center of the circle lies on the x-axis.The center of the circle lies on the y-axis.The standard form of the equation is (x – 1)² + y² = 3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

The radius of the circle is 3 units.

The center of the circle lies on the x-axis.

The center of the circle lies on the y-axis.

The standard form of the equation is (x – 1)² + y² = 3.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

On a coordinate plane, a circle has a center at (1, negative 2) and a radius of 4 units.