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Circles
Parabolas
Ellipses
Hyperbolas
Solving Quadratic & Linear Systems
100
(x-h)2+(y-k)2=r2
What is the equation of a circle?
100
y-k=a(x-h)2 In this equation for a parabola, if a>0, it opens________and if a<0, it opens_______.
What is upward and downward?
100
x2/a2+y2/ b2=1 and x2/b2+y2/a2=1. Both these equations are for ellipses with center____ with the first equation having a major axis that is____and the second equation having a major axis that is____.
What is (0,0), horizontal and vertical?
100
x2/a2-y2/b2=1 and y2/a2-x2/b2=1 Both of these equations are for a hyperbola with center___. The first equation has its foci on the_____ and the second equation has its foci on the______.
What is (0,0), x-axis, and y-axis ?
100
Solve this system using the substitution method: xy=8 and x2-y2=12
What is (4,2) and (-4,-2) ?
200
Find an equation of the circle with center (2, -5) and radius 8.
What is (x-2)2+(y+5)2=64
200
x-h=a(y-k)2 In this equation for a parabola, if a>0, it opens_____and if a<0, it opens________.
What is "to the right" and "to the left" ?
200
x2/16+y2/64=1 Find the x-intercept, y-intercept and the foci.
What is 4 and -4; 8 and -8; (0,-4sqr3) and (0,4sqr3)
200
y2/12-x2/4=1 In this hyperbola, find the y-intercepts and the foci.
What is sqr12, -sqr12 and what is (0,-4) and (0,4)?
200
Solve this system using the linear-combination method: x2+y2=25 and x2-y2=7.
What is (4,3), (4,-3), (-4,3), (-4,-3) ?
300
If the graph of the given equation is a circle, find its center and radius: x2+y2-4x+2y-4=0
What is (2,-1) and 3?
300
For this parabola y=(x+5)2, find the vertex and direction it opens.
What is (-5,0) and what is upward?
300
Find an equation of the ellipse with foci (-6,0) and (6,0) and sum of focal radii=18.
What is x2/81+y2/45=1
300
Find the equation of the hyperbola with asymptotes y=(3/2)x and y=(-3/2)x and foci (0,-sqr13) and (0,sqr13).
What is y2/9-x2/4=1 ?
300
The fence around a rectangular garden is 156m long. If the area of the garden is 1505m2, find the dimensions of the garden.
What is 35m by 43 m?
400
Find an equation of the circle described: center (0,5); passes through (0,0)
What is x2+(y-5)2=25 ?
400
Find an equation of the parabola that has Focus (0,2) and directrix x=2.
What is x-1=(-1/4)(y-2)2 ?
400
(x-h)2/a2+(y-k)2/b2=1 and (x-h)2/b2+(y-k)2/a2=1 Both of the ellipse equations have center____and the first equation has a ____major axis and the second equation has a _____major axis.
What is (h,k), horizontal, and vertical?
400
(x-h)2/a2-(y-k)2/b2=1 and (y-k)2/a2-(x-h)2/b2=1 Both of these equations are for a hyperbola with center___with the first equation having a____major axis and the second equation having a _____major axis.
What is (h,k), horizontal, and vertical?
400
Solve this system: x+2y-z=3 and 3y+z=-10 and -2z=8
What is 3, -2, -4 ?
500
Find the center and radius of the circle: 4x2+4y2-16x-24y+36=0
What is (2,3) and 2 ?
500
Consider the parabola x2+8y+4x-4=0 Find the vertex, focus, directrix, and axis of symmetry.
What is (-2,1), (-2, -1), y=3 and x=-2 ?
500
Find an equation of the ellipse with foci (-3,4) and (9,4) and sum of focal radii 14.
What is (x-3)2/49+(y-4)2/13=1
500
Find an equation of the hyperbola having foci (3,-8) and (3,-2) and difference of focal radii=4.
What is (y+5)2/4-(x-3)2/5=1
500
The theater sold $10 adult tickets, $5 children tickets, and $2.50 senior tickets. The number of senior tickets sold was 24 more than the number of children and adult tickets combined. There were 326 tickets sold, and the receipts totaled $1432.50. How many tickets of each type were sold?
What is 48 adult, 103 children, and 175 senior tickets?