Circles
What is the standard equation of a circle?
(x-h)^2+(y-k)^2=r^2
What is the standard form of a parabola (2 possibilities)?
y=a(x-h)^2+k
x=(y-k)^2+h
What is the standard form of a hyperbola (2 possibilities)?
(x-h)^2/a^2-(y-k)^2/b^2=1
(y-k)^2/a^2-(x-h)^2/b^2=1
What are the standard form of an ellipse (2 possibilities)
(x-h)^2/a^2+(y-k)^2/b^2=1
(y-k)^2/a^2+(x-h)^2/b^2=1
What are the four conic sections shapes?
Parabola, Circles, Ellipses, and Hyperbola
What is the equation of a circle centered at (4, -3) with a radius of 5?
(x-4)^2+(y+3)^2=25
In a parabola, what is the name of the line perpendicular to the directrix through the focus
axis of symmetry
Find the center and vertices of:
(x+1)^2/9-(y+2)^2/16=1
Center (-1, -2)
Vertices (2, -2), (-4, -2)
Find the vertices
(x-3)^2/36+(y+1)^2/9=1
Vertices: (-3, -1) and (9, -1)
Identify the conic section and find the domain and range.
x^2+y^2=49
A circle.
D={x|-7<=x<=7}
R={y|-7<=y<=7}
What is the equation of a circle with endpoints of the diameter (-4, 5) and (6, -3)?
(x-1)^2+(y-1)^2=41
What is the focus of the equation
x=-1/12(y+5)^2+2
(-1, -5)
Find the foci
(y-7)^2/4-x^2/32=1
Foci: (0, 13) and (0, 1)
Find the major and minor axis (equations) and the foci
(x+4)^2/25+(y+3)^2/16=1
minor: x = -4; major: y = -3
foci: (-1, -3), (-7, -3)
Identify the conic section and find the domain and range.
4x^2+25y^2=100
An ellipse.
D={x|-5<=x<=5}
R={y|-2<=y<=2}
What is the center and radius of the circle with the equation
x^2+y^2+6x-7=0
Center: (-3, 0); radius: 4
Find the vertex, focus, axis of symmetry and directrix in the equation of
x=1/12(y-2)^2-3
Vertex: (-3, 2); focus: (0, 2),
AOS: y=2; directrix: x=-6
Write the equation of a hyperbola with vertices (-3, -12), (-3, -4) and foci (-3, -15), (-3, -1)
(y+8)^2/16-(x+3)^2/33=1
Find the equation with major axis from (-6, 2) to (-6, -8) and minor axis from (-3, -3) to (-9, -3)
(y+3)^2/25+(x+6)^2/9=1
Without using the equation in standard form, state whether the graph is a parabola, ellipse, circle, hyperbola. Justify.
3x+9y^2-2y+4=0
Discriminant = 0: Parabola
What is the center and radius of the circle with the equation
x^2+y^2+8x-4y+11=0
Center: (-4, 2) and radius: 3
Write the equation in standard form
y=-1/4x^2+3x+6
y=-1/4(x-6)^2+15
What is the standard form of the hyperbola
25x^2-16y^2+100x+96y=444
(x+2)^2/16-(y-3)^2/25=1
Find the standard form of the equation:
4x^2+y^2-24x+4y+24=0
(y+2)^2/16+(x-3)^2/4=1
4y^2-36x^2=1
Identify the conic. Find the domain and range.
A hyperbola.
D= all real numbers
R={y|y>=0.5 or y<=-0.5}