Slay Kings and Queens
Write the standard form equation of a circle.
(x-h)2 + (y-k)2 = r2
Identify the conic section:
-x2 + 16y2 + 96y +128 = 0
Hyperbola
Given the equation (x-1)2 + (y+4)2 = 18, identify the radius and center.
Center: (1,-4)
Radius: 4.24
In a parabola, what does (h, k) give?
The vertex.
Convert into standard form and identify the conic section. 4x2 + 9y2 = 36
Ellipse. x2 / 9+ y2 / 4= 1
(x-3)2 + (y+2)2 = 25
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)
How do you recognize the transverse axis from the standard form of a hyperbola?
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
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.
Minor Axis
For the following:
y = 8(x-1)2 + 4
identify the vertex and the direction of opening.
Vertex: (1,4) and opens vertically (upwards).
Vertices
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.
If only one term is squared when given a conic section in general form, what conic section is it?
Parabola
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
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
If you are given a general equation with x2 as a term and -5y2 as a term, what is the conic section?
Hyperbola
Identify how far apart the two foci are:
((x2) / 625) + ((y2)/576) = 1
the foci are 14 units apart
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
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
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
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
Identify how far apart the two foci are:
((x2) / 100) + ((y2)/19) = 1
the foci are 18 units apart