Circles
What is the center of the circle
(x-3)^2+(y+1)^2=16
(3,-1)
Find the standard form of the equation of an ellipse with a center at (-4, -4) a vertex at (1,-4) and a minor axis length of 8.
((x+4)^2)/9-((y+1)^2)/4=1
The golf channel uses a parabolic microphone to capture all the sounds from golf tournaments. If one of its microphones has a parabolic surface generated by the parabola x^2=12y, locate the focus (electronic receiver) of the parabola.
(0,3)
What is the equations of the asymptotes of the hyperbola
x^2/4-y^2/9=1
y=+-3/2x
Eliminate the parameter
x=t-1
y=t^2-2
y=(x+1)^2-2
Which equation is an equation of a circle?
1) 3y^2+8y-4x^2-2x+6=0
2) 5x^2+5x+10y^2+3y=9
3) 4y^2+5x+4x^2-8y=-6
4) 5x^2+5x-5y^2+4y+7=0
3
Which equation represents an ellipse?
1) 6x^2-12x-3y^2+6y-13=0
2) 8y^2-4x^2+8x-16y-7=0
3) 10x^2+5y^2+5x-10y+17=0
3
Find the equation of the standard form of the parabola with a vertex at (0,0) and the directrix at x=3
y^2=-12x
Which equations represent hyperbolas?
1) 6x^2-12x-3y^2+6y-13=0
2) 8y^2-4x^2+8x-16y-7=0
3) 10x^2+5y^2+5x-10y+17=0
1 and 2
Find the rectangular equation
x=4cost
y=6sint
x^2/16+y^2/36=1
(x-4)^2+(y-3)^2=25
Which equation(s) is(are) a(n) ellipse(s)
1) 2x^2+4x-9y-18=0
2) 5x^2+4y^2+10x+8y+9
3) 3y^2+3x^2-6y-9=0
2 and 3
Which equation is a parabola
1) 2x^2+4x-9y-18=0
2) 5x^2+4y^2+10x+8y+9
3) 3y^2+3x^2-6y-9=0
1
Find the standard form of the hyperbola by completing the square.
9x^2-5y^2-54x-40y-44=0
((x-3)^2)/5 - ((y+4)^2)/9 = 1
Eliminate the parameter and obtain the standard form of the rectangular equation
x=-5t-4
y=-6t-3
y=(-6/5)x-(9/5)
What is the radius of the circle x^2+4x+y^2-21=0
5
Find an equation in standard form for the ellipse whose major axis endpoints are (-5,2) and (3,2) and whose minor axis has length 6
((x+1)^2/16+((y-2)^2)/9=1
Find the standard form of the equation of the parabola with a vertex at (2,-3) and a focus at (2,-5)
(x-2)^2=-8(y+3)
((x-5)^2)/144 - ((y+2)^2)/256 = 1
Write the rectangular equation for
x=8cost
y=8sint
x^2+y^2=64
What is the center and radius of the circle 2x^2+2y^2-8x-24y+28=0
(2,6) r=sqrt(26)
Find the standard form of the equation of an ellipse with foci at (1,7) and (1,-1) with a major axis length of 10
((x-1)^2)/9 + ((y-3)^2)/25 = 1
What is the vertex of the parabola -3y^2-10x+10=0 and which way does is open?
Vertex is (1,0), opens towards the left
Find the vertices, foci and the equations of the asymptotes of the hyperbola
y^2/9 - x^2/4 = 1
Vertices (0,3) (0,-3)
foci (0, sqrt(13)) (0, -sqrt(13))
Asymptotes y=+-3/2x
Ms. J hit a baseball at 5 feet above the ground with an initial speed of 100 feet per second at an angle of 20 degrees with the horizontal. Use the equations below to write the parametric equations that represent the motion of the baseball.
x(t)=(vcos(theta))t
y(t)=-16t^2+(vsin(theta))t+(initial height)
x(t)=100cos(20)t
y(t)=-16t^2+(100sin(20))t+5