Conic Sections Parabolas and Ellipse

Conic Sections: Parabolas

By Patty Ashe

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Multiple Choice

Given the parabola: $$\left(x+1\right)^2=8\left(y\ -\ 1\right)$$

What is its orientation?

• Vertical - Up

• Vertical - Down

• Horizontal - Right

• Horizontal - Left

Fill in the Blank

Given the parabola: $$\left(x+1\right)^2=8\left(y\ -\ 1\right)$$

What is it's vertex?

Write your answer with no spaces.

(

-

,

)

Fill in the Blank

Given the parabola: $$\left(x+1\right)^2=8\left(y\ -\ 1\right)$$

What is its directrix?

Write your answer with no spaces.

=

-

Fill in the Blank

Given the parabola: $$\left(x+1\right)^2=8\left(y\ -\ 1\right)$$

What is its axis of symmetry?

Write your answer with no spaces.

=

-

Graphing

Graph the parabola: $$\left(x+1\right)^2=8\left(y\ -\ 1\right)$$

Multiple Choice

Given the parabola: $$\left(y-2\right)^2=-4\left(x\ -\ 3\right)\$$

What is its orientation?

• Vertical - Up

• Vertical - Down

• Horizontal - Right

• Horizontal - Left

Fill in the Blank

Given the parabola: $$\left(y-2\right)^2=-4\left(x\ -\ 3\right)\$$

What is its vertex?

Write your answer with no spaces

(

,

)

Fill in the Blank

Given the parabola: $$\left(y-2\right)^2=-4\left(x\ -\ 3\right)\$$

What is its focus?

Write your answer with no spaces

(

,

)

Fill in the Blank

Given the parabola: $$\left(y-2\right)^2=-4\left(x\ -\ 3\right)\$$

What is its directrix?

Write your answer with no spaces

=

Fill in the Blank

Given the parabola: $$\left(y-2\right)^2=-4\left(x\ -\ 3\right)\$$

What is its axis of symmetry?

Write your answer with no spaces

=

Draw

Graph the parabola: $$\left(y-2\right)^2=-4\left(x\ -\ 3\right)$$

Math Response

Write the equation of a parabola that has a vertex (-1, 5), contains the point (-5, 3) and opens to the left.

Type answer here

Correct Answer: \left(y-5\right)^2=-1\left(x+1\right)

Deg^°

Rad

Conic Sections: Ellipse

By Patty Ashe

Multiple Choice

Given the ellipse: $$\frac{\left(x-1\right)^2}{25}+\frac{\left(y+2\right)^2}{16}=1$$

What is its orientation?

• horizontal

• vertical

• Both - Its a circle

Fill in the Blank

Given the ellipse: $$\frac{\left(x-1\right)^2}{25}+\frac{\left(y+2\right)^2}{16}=1$$

What is its center?

Write your answer with no spaces!

(

,

-

)

Categorize

Options (4)

(-4, -2)

(6, -2)

(1, -6)

(1, 2)

Given the ellipse: $$\frac{\left(x-1\right)^2}{25}+\frac{\left(y+2\right)^2}{16}=1$$

Match the points

Vertices (ends of major axis)

Co-vertices (ends of minor axis)

Math Response

Given the ellipse: $$\frac{\left(x-1\right)^2}{25}+\frac{\left(y+2\right)^2}{16}=1$$ .

Find the value of c

Type answer here

Correct Answer: 3

Deg^°

Rad

Draw

Graph the ellipse: $$\frac{\left(x-1\right)^2}{25}+\frac{\left(y+2\right)^2}{16}=1$$

Multiple Choice

Given the ellipse: $$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{9}=1$$

What is its orientation?

• horizontal

• vertical

• Both - its a circle!

Fill in the Blank

Given the ellipse: $$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{9}=1$$

What is its center?

Write your answer with no spaces

(

-

,

)

Categorize

Options (4)

(0,2)

(-6, 2)

(-3,-1)

(-3, 5)

Given the ellipse: $$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{9}=1$$

Match the points

Vertices (ends of horizontal axis)

Co-vertices (ends of verticals)

Math Response

Given the ellipse: $$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{9}=1$$ .

Find the value of c

Type answer here

Correct Answer: 0

Deg^°

Rad

Math Response

Given the ellipse: $$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{9}=1$$ .

What is the radius?

Type answer here

Correct Answer: 3

Deg^°

Rad

Draw

Graph the ellipse: $$\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{9}=1$$