Conics Anatomy
Equations YOU Should Know
Circles
Ellipses
100
The name of the distance between an endpoint and the center of a circle.
Radius
100
The formula to find the Focus points
c^2=a^2-b^2
100
What is the Radius of the following circle
x^2+(y-3)^2=7
sqrt7
2.65
100
Is this a vertical or horizontal Ellipse?
(x-2)^2/16+(y+3)^2/9=1
Horizontal
200
The longer of the two Axis of Symmetry on an Ellipse.
Major Axis
200
The Midpoint Formula
((x_1+x_2)/2,(y_1+y_2)/2)
200
What is the Center of this Circle
(x+2)^2+(y-1)^2=4
(-2,1)
200
What is the "a" value of the following ellipse.
(x-1)^2/16+(y+4)^2/36=1
a=6
300
The Endpoints on the Minor Axis are known as the
Co-Vertices
300
The Standard Form of a Circle
Centered at (h,k)
(x-h)^2+(y-k)^2=r^2
300
Write the Equation for this Circle
(x-4)^2+(y+5)^2=36
300
What is the equation for a Horizontal Ellipse with the following characteristics.
Center (4,1)
a=3
b=2
(x-4)^2/9+(y-1)^2/4=1
400
The Vertices are __ units away from the center
+-a
400
The Distance Formula
d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)
400
What is the equation for a circle with a center at (3,-1) and a radius
4sqrt3
(x-3)^2+(y+1)^2=48
400
What is the equation for an ellipse with the following characteristics.
Vertices: (2,7) and (2,-9)
Foci: (-4,-1) and (8,-1)
(x-2)^2/100+(y+1)^2/64=1
500
The sum of the distance from any endpoint on the ellipse from these fixed points remains constant
Foci
500
The Standard Form of a Vertical Ellipse
Centered at (h,k)
(x-h)^2/b^2+(y-k)^2/a^2=1
500
What is the equation for a circle with diameter endpoint at (-13,-7) and (11,11)
(x+1)^2+(y-2)^2=225
500
What are the Co-vertices of this Ellipses
4x^2+9y^2=16x+20
(2,–2),(2,2)