Classify each conic section.
x 2+ y2 = 30
Circle
−x2 + 10x + y − 21 = 0
y = (x − 5)2 − 4
Center: (8, 2) Radius: 6
(x - 8)2+ ( y - 2)2 = 36
(x - 5)2 /4 + ( y + 1)2 /36 = 1
Center: (5, -1) Vertices: (5, 5) (5, -7) Co-vertices: (7, -1) (3, -1)
x = y2
Parabola
3x2 + 30x + y + 79 = 0
y = −3(x + 5)2 − 4
Center: (9, 12) Radius: 2 sqr 10
(x - 9)2+ ( y - 12)2 = 40
x 2 /49 + ( y - 1)2 /36 = 1
Center: (0, 1) Vertices: (7, 1) (-7, 1) Co-vertices: (0, 7) (0, -5)
x = (y + 4)2 − 2
Parabola
−9x2 + y2 − 72x − 153 = 0
y2/ 9 − (x + 4)2 = 1
Center: (10, -4) Radius: 6
x - 10)2 + ( y + 4)2 = 36
(x + 4)2 /9 + ( y + 3)2 /16 = 1
Center: (-4, -3) Vertices: (-4, 1) (-4, -7) Co-vertices: (-1, -3) (-7, -3)
y2 /25 − x2/ 25 = 1
Hyperbola
−y2+ x + 8y − 17 = 0
x = (y − 4)2 + 1
Center: (3, 16) Point on Circle: (2, 16)
(x - 3)2 + ( y - 16)2 = 1
(x + 5)2 /4 + y 2 /36 = 1
Center: (-5, 0) Vertices: (-5, 6) (-5, -6) Co-vertices: (-3, 0) (-7, 0)
(x − 1)2 + y ^2/ 25 = 1
Ellipse
−2y2 + x − 20y − 49 = 0
x = 2(y + 5)2 − 1
Center: (16, 15) Point on Circle: (16, 17)
(x - 16)2 + ( y - 15)2 = 4
4x 2 + 49y 2 + 196y = 0
Center: (0, -2) Vertices: (7, -2) (-7, -2) Co-vertices: (0, 0) (0, -4)