Learning Task - Ellipse

The major axis is:

• The shorter axis of an ellipse
• The longer axis of an ellipse
• The closest point closest to the Sun
• The farthest point closest to the Sun

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

• (-8, 10); a = 12, b = 6
• (-8, 10); a = 6, b = 12
• (8, -10); a = 12, b = 6
• (8, -10); a = 6, b = 12

Tags

CCSS.HSG.GPE.A.1

The standard form of an ellipse is:

• $\left(x-h\right)^2+\left(y-k\right)^2=r^2$

• $\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1$

• $\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1$

• $x=a\left(y-h\right)^2+k$

What are the vertices of the ellipse?

• (0, 0)
• (7, 1) and (-1, 1)
• (3, -5) and (3, 7)
• (3, 1)

The major axis of the ellipse with equation $\frac{x^2}{169}+\frac{y^2}{49}=1$  is...

• the x-axis

• the y-axis

• both x and y-axis

• no axis

What is the center of the ellipse with equation  $\left(x-1\right)^2+\frac{y^2}{25}=1$ ? 

• (0, 0)

• (1, 5)

• (1, 0)

• (0, 1)

Identify the center and the values of a and b for the ellipse with the equation  $\frac{x^2}{25}+\frac{y^2}{4}=1$  ?

• C(0,4), a= 25, b=4

• C(0,0), a= 4, b=25

• C(0,5), a= 2, b=5

• C(0,0), a= 5, b=2

What are the foci of the ellipse with equation  $\frac{\left(x+3\right)^2}{4}+\frac{\left(y-1\right)^2}{1}=1$  ?

• (-5,1) and (-1,1)

•  $\left(\sqrt{3},0\right)$  and  $\left(-\sqrt{3},0\right)$  

• (0,1) and (-6,1)

•  $\left(\sqrt{3}-3,1\right)$  and  $\left(-\sqrt{3}-3,1\right)$  

What are the co-vertices of the ellipse?

• (0, 0)

• (7, 1) and (-1, 1)

• (3, -5) and (3, 7)

• (3, 1)

Which statement is TRUE?

• This is a tall ellipse.

• This is a wide ellipse.

• The length of the major axis is 36.

• The length of the minor axis is 1.