9.1 The Ellipse

​9.1 The Ellipse

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Multiple Choice

Planets orbit the Sun in a shape called a(n)...#30

• circle

• ellipse

• focus

• perihelion

Multiple Choice

Which of the following represents and equation of an ellipse? #34

• $$x^2=16y$$

• $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$

• $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$

• $$\frac{x}{b^2}+\frac{y}{a^2}=1$$

Multiple Choice

The line containing the center and foci. #20

• Major Axis

• Minor Axis

• Vertices

• Co-Vertices

Multiple Choice

An ellipse centered at the origin has a vertical major axis length of 8 units and a horizontal minor axis length of 4. What is the equation of the ellipse? #23

• $$\frac{x^2}{4}+\frac{y^2}{16}=1$$  

• $$\frac{x^2}{16}+\frac{y^2}{4}=1$$  

• $$\frac{x^2}{16}+\frac{y^2}{64}=1$$  

• $$\frac{x^2}{64}+\frac{y^2}{16}=1$$  

Multiple Select

Which of the following equations represents an ellipse? #33

• $$\frac{\left(x+1\right)^2}{4}+\frac{\left(y-2\right)^2}{9}=1$$

• $$\frac{x^2}{25}+\frac{y^2}{9}=1$$

• $$\left(x+1\right)^2+4\left(y-2\right)^2=16$$

• $$\frac{\left(x-3\right)^2}{4}-\frac{\left(y+2\right)^2}{9}=1$$

Multiple Choice

In an ellipse, what is the length of the major axis? #35

• a

• 2a

• b

• 2b

Multiple Choice

Find the standard equation of the given ellipse. #3

Multiple Choice

What are the co-vertices of the given ellipse? #4

• $$\left(5,\ -4\right)\ and\ \left(5,\ 2\right)$$

• $$\left(-2,\ -1\right)\ and\ \left(12,\ -1\right)$$  

• $$\left(-1,\ -2\right)\ and\ \left(-1,\ 12\right)$$

• $$\left(-4,\ 5\right)\ and\ \left(2,\ 5\right)$$

Multiple Choice

What is the center of the ellipse? #5

• (0, 0)

• (1, 5)

• (1, 0)

• (0, 1)

Multiple Choice

What are the vertices of the ellipse? #7

• (0, 0)

• (7, 1) and (-1, 1)

• (3, -5) and (3, 7)

• (3, 1)

Multiple Choice

What is the center, a and b values for the following equation: x² + 4y² + 16x - 80y + 320 = 0 #8

• (-8, 10); a = 12, b = 6

• (-8, 10); a = 6, b = 12

• (8, -10); a = 12, b = 6

• (8, -10); a = 6, b = 12

Multiple Choice

Find the standard equation of the given ellipse. #17

Multiple Choice

The graph of an ellipse is shown. Which equation represents this ellipse? #24

• $$\frac{\left(x-1\right)^2}{16}+\frac{\left(y+1\right)^2}{36}=1$$

• $$\frac{\left(x-1\right)^2}{36}+\frac{\left(y+1\right)^2}{16}=1$$

• $$\frac{\left(x+1\right)^2}{16}+\frac{\left(y-1\right)^2}{36}=1$$

• $$\frac{\left(x+1\right)^2}{36}+\frac{\left(y-1\right)^2}{16}=1$$

Multiple Choice

The graph of an ellipse is shown. Which equation represents this ellipse? #25

• $$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{25}=1$$

• $$\frac{\left(x-3\right)^2}{25}+\frac{\left(y+2\right)^2}{9}=1$$

• $$\frac{\left(x-3\right)^2}{9}+\frac{\left(y+2\right)^2}{25}=1$$

• $$\frac{\left(x+3\right)^2}{25}+\frac{\left(y-2\right)^2}{9}=1$$

Multiple Choice

Write an equation for the ellipse with each set of characteristics. Then answer the question. Vertices ( 4, 3), (4, - 9) Length of the minor axis is 8. What is the center of this ellipse? #19

• (4, 6)

• ( - 4, 3)

• (6, 4)

• (4, -3)

Multiple Choice

Write an equation for the ellipse with each set of characteristics. Then answer the question. Vertices ( -7, -3), (13, - 3) foci ( - 5, -3 ), (11, -3). What is the a and b value of the ellipse? #21

• a = 10 , b = 6

• a = 6 , b = 10

• a = 36 , b = 100

• a = 100 , b = 36

Multiple Choice

Write the equation of an ellipse that has a major axis of 12 units in length, with foci at  $$\left(\pm5,\ 0\right)$$  . #29

• $$\frac{\left(x-5\right)^2}{36}+\frac{\left(y+5\right)^2}{11}=1$$  

• $$\frac{x^2}{11}+\frac{y^2}{36}=1$$  

• $$\frac{x^2}{36}+\frac{y^2}{11}=1$$  

• $$\frac{\left(x+5\right)^2}{11}+\frac{\left(y-5\right)^2}{36}=1$$