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circles
parabolas
hyperbolas
ellipse
vocab
100
find the center and radius (x-2)^2+(y+1)^2=16
Center=(2,-1) Radius=4
100
what is the definition of a parabola?
is the set of points in the plane that are equidistant from a point (the focus) and a line (the directrix.)
100
what is the difference between a parabola and a hyperbola?
in a hyperbola x&y are both squared
100
find the center of 9x^2+y^2=36
center=(0,0)
100
what is the definition of a circle
a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
200
write the equation center:origin, radius:8
x^2+y^2=64
200
what is the distance from vertices to focus
P
200
In the standard equation for a hyperbola which comes first b^2 or a^2?
a^2
200
find the vertices and co-vertices of x^2/81+y^2/49=1
vert:(0,0) (-9,0) covert:(0,7) (0,-7)
200
what is the definition of the minor axis
the shorter or shortest axis of an ellipse
300
Write the equation when the center is (0,11) diameter:8
x^2+(y-11)^2=16
300
find the equation of a parabola given the focus and directrix x&y focus:(0,-4) directrix: y=x
y= -1/16x^2
300
write the equation when given the vertices and foci vertices: (-2,1) (2,1) foci: (-3,1) (3,1)
x^2/9-(y-1)^2-1/5=1
300
find the foci of (x-3)^2/9+(y+2)^2/25=1
(3,2) (3,-6)
300
what is the definition of a Foci
a point having the property that the distances from any point on a curve to it and to a fixed line have a constant ratio for all points on the curve
400
rewrite the equation and find the center and radius x^2-14x+y^2-8y=28
(x-7)^2+(y-4)^2=36
400
find the equation of a parabola given the focus and directrix x&y focus:(2,2) directrix: y=-2
y=1/8(x-2)^2
400
write the equation when given the vertices and asymptotes vertices: (0,±3) asymptotes: y=±3x
y^2/9-x^2/1=1
400
find the center,vertices,co-vertices and foci of (x-1)^2/25+(y-1)^2/9=1
Center=(1,1) vert=(6,1) (-4,1) covert=(1,4) (1-2,) foci=(5,1) (-3,1)
400
what is the definition of a major axis
it is the longest diameter a line segment that runs through the center and both foci, with ends at the widest points of the perimeter.
500
what are the degrees and radians of the unit circle along with the corresponding points?
0° 0π,30° π/6,45° π/4,60° π/3,90° π/2,120° 2π/3, 135° 3π/4,150° 5π/6,180° π,210° 7π/6,225° 5π/4, 240° 4π/3,270° 3π/2,300° 5π/3,315° 7π/4,330° 11π/6, 360° 2π,sin(0°) 0,sin(30°) 1/2,sin(45°) √2/2, sin(60°) √3/2,sin(90°) 1,sin(120°) √3/2,sin(135°) √2/2, sin(150°) 1/2,sin(180°) 0,sin(210°) −1/2,sin(225°) −√2/2, sin(240°) −√3/2,sin(270°) −1,sin(300°) −√3/2, sin(315°) −√2/2,sin(330°) −1/2,sin(360°) 0,cos(0°) 1, cos(30°) √3/2,cos(45°) √2/2,cos(60°) 1/2,cos(90°) 0, cos(120°) −1/2,cos(135°) −√2/2,cos(150°) −√3/2, cos(180°) −1,cos(210°) −√3/2,cos(225°) −√2/2, cos(240°) −1/2,cos(270°) 0,cos(300°) 1/2, cos(315°) √2/2,cos(330°) √3/2,cos(360°) 1,cos(π/6) √3/2,cos(π/4) √2/2,cos(π/3) 1/2,cos(π/2) 0,cos(2π/3) −1/2,cos(3π/4) −√2/2,cos(5π/6) −√3/2,cos(π) −1,cos(7π/6) −√3/2,cos(5π/4) −√2/2,cos(4π/3) −1/2, cos(3π/2) 0,cos(5π/3) 1/2,cos(7π/4) √2/2,cos(11π/6) √3/2,cos(2π) 1,sin(π/6) 1/2,sin(π/4) √2/2,sin(π/3) √3/2, sin(π/2) 1,sin(2π/3) √3/2,sin(3π/4) √2/2,sin(5π/6) 1/2, sin(π) 0,sin(7π/6) −1/2,sin(5π/4) −√2/2,sin(4π/3) −√3/2, sin(3π/2) −1,sin(5π/3) −√3/2,sin(7π/4) −√2/2,sin(11π/6) −1/2,sin(2π) 0
500
find the focus and directrix of the parabola y-2=1/12(x+7)^2
focus:(-7,5) directrix: y=3
500
put the following into standard form and find the center,vertices and foci
(x-2)^2/1-(y+3)^2/9=1 center:(2,-3) vertices:(1,-3) (3,-3) foci: (2±√(10),-3)
500
An ellipse is given by the equation 8x^2 + 2y^2 = 32 Find the major axis and the minor axis of the ellipse and their lengths, the vertices of the ellipse, and the foci of this ellipse.
x^2 / 4 + y^2 / 16 = 1 major:8 minor:4 vertices:(0 , 4) (0 , -4) foci:(0 , 2√3) and (0 , -2√3)
500
what is the definition of a conic section
focus of all points such that they are equidistant from a point, known as the focus, and a straight line, called the directrix.