Slay Kings and Queens
Write the standard form equation of a circle.
(x-h)2 + (y-k)2 = r2
What is the equation of the hyperbola? Focus: (±-5,0) Vertices: (±4,0)
x2/16-y2/9=1
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.
(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
Minor Axis
Find the vertices and foci of the hyperbola 3x2-4y2=12
Vertices: (±2,0) Foci: (±√7,0)
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.
A symmetrical open curve formed by the intersection of a circular cone
What is a 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
(x-h)^2/a^2+(y-k)^2/b^2=1 for ellipse with horizontal major axis and (x-h)^2/b^2+(y-k)^2/a^2=1 for ellipse with vertical major axis
What are the standard equations for an ellipse?
The center point of this ellipse (x+8)^2/9^2+(y-3)^2/7^2=1
What is (-8, 4)?
The vertices of the hyperbola with the question of -y^2/25-x^2/26=1
What is (0,5)(0,-5)
The foci equation of a hyperbola
What is C^2=A^2+B^2
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