Circles
Distance/Midpoint/Circles
Ellipses
Parabolas
100
Identify the center and radius of the circle with equation (x-2)^2+(y+5/2)^2=25
Center: (2,-5/2) Radius = 5
100
Find the distance between the two points and the midpoint: (-3,7), (1,-1)
distance: 4√(5)
midpoint: (-1,3)
100
Graph the ellipse x2/9 + y2/4 =1 and find the vertices, co-vertices, length of major axis, length of minor axis, and foci.
Vertices: (3, 0), (-3,0)
Co-vertices: (0, 2), (0, -2)
Major: 6 units
Minor: 4 units
Foci: (√5, 0), (-√5, 0)
100
Find an equation of a parabola with directrix y = 6 and focus (0,2).
x2 = -8(y-4)
200
Identify the center and radius of the circle by completing the square:
x^2+6x+y^2-10y=2
Center: (-3,5) Radius:
6
200
Find the distance between the two points and the midpoint: (-a,b),(2a,4b)
midpoint:
(\frac{a}{2}, \frac{5b}{2})
distance:
3\sqrt{a^2+b^2}
200
Graph and find the length of the major axis, length of the minor axis, center, vertices, co-vertices, and foci for the ellipse.
4x2 + y2 -8x + 6y - 23 = 0
ellipse: (x-1)2/9 + (y+3)2/36 = 1
Major axis: 12
Minor axis: 6
Center: (1, -3)
co-vertices: (-2, -3), (4, -3)
Vertices: (1, 3), (1, -9)
Foci: (1, -3±3√(3))
200
Find the equation of the parabola with vertex (3, -2) and directrix at x = 4
x = -1/4(y+2)2+ 3
300
Find the equation of the circle with center (-1,9) and radius
2sqrt6
(x+1)^2+(y-9)^2=24
300
Graph and find the center and radius of the circle with the equation: x2 +y2+6x-8y-119 = 0
(-3, 4); 12
300
Find an equation of the ellipse with vertices as (6, 4) and (-4,4) and co-vertices (1, 4 + √3) and (1, 4 - √3)
(x-1)2/25 +(y-4)2/3 = 1
300
Graph (x-1)2 = -8(y+1). Label the vertex, focus, and directrix.
directrix: y = 1
Vertex: (1, -1)
Focus: (1,-3)
400
Identify the center and radius of the circle with equation
3x^2+3y^2-12x+18y=0
Center: (2,-3) Radius:
sqrt13
400
Find an equation of a circle whose diameter has endpoints (0,3) and (4,-3).
(x-2)2 +y2 =13
400
Find an equation of the ellipse with foci (6,2) and (-10, 2) and with 20 as the length of the major axis.
(x+2)2/100 + (y-2)2/36 = 1
400
Find the vertex, focus, and directrix of the parabola: y2+8y -12x + 4 = 0
(-1,-4), (2,-4), x = -4
500
Find an equation of the circle tangent to both coordinate axes and the line x=8 .
(x+4)^2 +(y-4)^2 = 16 or (x+4)^2 +(y+4)^2 = 16
500
Suppose that a = b in the equation x2/a2 + y2/b2 = 1. What is the value of c? Where are the foci? What special ellipse is this?
c is 0 so the foci are at the origin and it is a circle.
500
Graph x - 11 = y2 + 6y and find the vertex, focus, and directrix
V: (2,-3)
F: (2 1/4, -3)
D: x = 1 3/4
