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Classifying Conics
Hyporbola
Parabola
Circle
Ellipse
100
3y^2+x-30y+74=0
Parabola
100
Find the Equation Vertices (0,4) (0,-4) Endpoints of conjugate Axis (2,0) (-2,0)
(y^2/16)-(x^2/4)=1
100
Which Direction x^2=-4y
UP
100
Find the equation x^2=r^2-y^2 R=9
x^2+y^2=81
100
Does the point equal the equations ? Point(8,8) x^2+y^2+18x+9y+74=0 -2x-y+10=0
NO
200
x^2+y^2+4x+2y-4=0
Circle
200
Find the Equation Vertices (2,10) (2,-8) Perimiter of Central Rectangle = 44
((y-1)^2/81)-((x-2)^2/4)=1
200
Find the Equation Open UP or DOWN Vertex (5, -2) Pass Through (3, -1)
(x-5)^2 = 4 (y+2)
200
Find the Equation Radius=Square root of 13 Center (-1,2)
(x+1)^2+(y-2)^2=13
200
Does the point fit the equations ? x^2+y^2-12x+3y-17=0 2y-4x=0
NO
300
16x^2-9y^2+64x+18y-89=0
Hyporbola
300
Find the Equation 4x^2-9y^2=36
(x^2/9)-(y^2/4)=1
300
Find the Equation Vertex at Origin Diretrix ~ x=(1/16)
y^2 = (-1/4)x
300
Find the Equation Center (0,0) Radius =81
x^2+y^2=6561
300
Find the Equation Vertices (-4,0) (4,0) Covertices (0,-3) (0,3)
(x^2/16)+(y^2/9)=1
400
4x^2+25y^2+100y=0
Ellipse
400
Horizontal or Veritcal Find A,B,C Center Vertices Co-Vertices Focus Asyomtope Trans & Con (x^2/9)-(y^2/4)=4
Horizontal A ~ 3 B ~ 2 C ~ Square Root of 13 Center (0,0) Vertices (3,0) (-3,0) Co-Vertices (0,2) (0,-2) Focus (+- Square Root of 13,0) Asyomtope y= +-(2/3)x Trans ~ 6 Con ~ 4
400
Direction Vertex P Focus Axis of Symm Directix Max/Min y^2=2x
Direction ~ Right Vertex (0,0) P = (1/2) Focus (0,(1/2)) Axis of Symm ~ x=0 Directix ~ x = (-1/2) Max/Min ~ Min 0
400
Find the new Transition (x+5)^2+(y-8)^2=32 Translate: 2 Left 4 Up
(x+7)^2+(y-12)^2=32
400
Find the Equation 3x^2+3y^2=48
(x^2/16)+(y^2/16)=1
500
x^2-4x+2y+12=0
Parabola
500
Horizontal or Veritcal Find A,B,C Center Vertices Co-Vertices Focus Asyomtope Trans & Con ((y-2)^2/16)-((x-1)^2/4)=1
Veritcal A ~ 4 B ~ 2 C ~ 2 Square Root of 5 Center (1,2) Vertices (1,6) (1,-2) Co-Vertices (3,2) (-1,2) Focus ( 1, 2 +- 2 Square Root of 5 Asyomtope (y-2)=+-2 (x-1) Trans ~ 8 Con ~ 4
500
tyyDirection Vertex P Focus Axis of Symm Directix Max/Min -4(y+2) = (x-5)^2
Direction ~ Down Vertex (5,-2) P = -1 Focus (5,-3) Axis of Symm ~ x=5 Directix ~ y= 1 Max/Min ~ Max -2
500
Find the Equation Center lies in the 2nd Quadrant Tangent to x=2, x=8, y=3, y=0
(x-5)^2+(y+2)^2=25
500
Solve the System 3x^2+2y^2=35 4x^2-3y^2=24
(3,2)