Show:
Slay Kings and Queens
No Cap- you aren't cooked
Periotttt.
Vibe Check: Do you know your conics?
Conics are living rent free in my head
100

Write the standard form equation of a circle. 

(x-h)2 + (y-k)2 = r2

100

Identify the conic section: 

-x2 + 16y2 + 96y +128 = 0

Hyperbola 

100

Given the equation (x-1)2 + (y+4)2 = 18, identify the radius and center.

Center: (1,-4) 

Radius: 4.24

100

In a parabola, what does (h, k) give?

The vertex.

100

Convert into standard form and identify the conic section. 4x2 + 9y2 = 36

Ellipse. x2 / 9+ y2 / 4= 1

200
Write the standard form of a circle with a center at (3,-2) and a radius of 5.

(x-3)2 + (y+2)2 = 25

200

Write the equation of a parabola with vertex at (2, 3) that opens upwards and has a focal length of 4.

(x-2)2 =16(y-3)

200

How do you recognize the transverse axis from the standard form of a hyperbola? 

The positive variable.
200

Write the standard form of an ellipse and hyperbola. Clearly label each one. 

Ellipse:

((x-h)2  / a2 )+((y-k)2 / b2)= 1

Hyperbola: 

((x-h)2  / a2 )-((y-k)2 / b2)= 1

200

Give the definition of a major and minor axis. 

The major axis is the longest axis of symmetry in an ellipse and the minor is the shortest axis of symmetry. 

300
In an ellipse, co-vertices are endpoints for which axis?

Minor Axis

300

For the following:

y = 8(x-1)2 + 4

identify the vertex and the direction of opening. 

Vertex: (1,4) and opens vertically (upwards).

300
If the x variable of a hyperbola is positive, the axis given by this would contain the endpoints known as?

Vertices 

300

How do you know if an ellipse is horizontal or vertical?

The larger denominator is under the x variable if the ellipse is horizontal. The larger denominator is under the y variable if the ellipse is vertical.

300

If only one term is squared when given a conic section in general form, what conic section is it?

Parabola

400

Convert the following to standard form and state the conic section: 

-25x2+36y2+100x+360y-100= 0

((y+5)2/25) - ((x-2)2/36) = 1

hyperbola

400

Convert the following to standard form and identify the conic section.

x2+y2−6x−8y+9=0

Circle. (x-3)2+(y-4)2 = 16

400

If you are given a general equation with x2 as a term and -5y2 as a term, what is the conic section? 

Hyperbola 

400

Identify how far apart the two foci are: 

((x2) / 625) + ((y2)/576) = 1

the foci are 14 units apart

500

What is the standard form of the horizontal ellipse with center at the origin, a major axis of length 10, and a minor axis of length 6?

((x2)/25) + ((y2)/9)=1

500

The Oval Office of the President of the United States is elliptical. It measures 50 feet wide and 98 feet long.  If a person is standing at one focus, his whisper can be heard by a person standing on the other focus.

Write the equation of the ellipse using the origin as the center of the office.

How far apart of the two people?

84.29 ft apart

500

The major axis is horizontal, with a center at (0,0), a major axis that is 12 units long, and a minor axis that is 4 units long, write the standard form equation of the ellipse. 

((x2) / 36) + ((y2) / 4) = 1

500

Given a horizontal ellipse, with a center at (0,0), major axis of length 6, and a minor axis of length 4, write the equation. 

((x2)/9) + ((y2)/4) = 1

500

Identify how far apart the two foci are: 

((x2) / 100) + ((y2)/19) = 1

the foci are 18 units apart