Circles
What is the standard form equation of a circle with center at (0, 0) and radius 4?
x² + y² = 16
The equation (x + 3)² = 12(y − 2) represents a parabola opening:
Up
Which equation represents an ellipse centered at the origin with major axis along the x-axis?
x²/a² + y²/b² = 1
The equation x²/25 − y²/9 = 1 represents a hyperbola opening:
Left and right
A circle has center at (2, -1) and radius 6. Find the equation.
(x − 2)² + (y + 1)² = 36
In the equation y² = 8x, what is the distance between the vertex and the focus?
2
Which of the following is true about ellipse?
A. a= bigger number and major axis, b= smaller number and minor axis.
B. a= bigger number and minor axis, b= smaller number and major axis.
C. a= smaller number and minor axis, b= bigger number and major axis.
A. a= bigger number and major axis, b= smaller number and minor axis.
a=9, b^2=9, find c
√90
What is the equation of a circle with center at (3, -2) and radius 5?
(x - 3)² + (y + 2)² = 25
A parabola has vertex at the origin and focus at (0, 4). What is its equation?
x² = 16y
What is the value of b in the equation x²/49 + y²/25 = 1
5
For the hyperbola -x²/16 + y²/9 = 1, the length from the center to one endpoint of the transverse axis is:
B. 3
Does the point (7, 4) lie inside, on, or outside the circle:
(x - 2)² + (y - 1)² = 25
Outside the circle
For the parabola y² = 16x, what is the length of the latus rectum?
16
. In the ellipse x²/100 + y²/64 = 1, find the distance between the foci.
12
In the hyperbola x²/36 − y²/64 = 1, find c.
10
A circle has its center at (2, -3) and radius 5. Which of the following points lies on the circle?
A. (7,-3)
B. (7,3)
C. (-7,3)
D. (-7,-3)
A. (7,-3)
A spotlight is shaped like a parabola with its bulb at the focus (0, 3) and vertex at (0, 0). If the reflector is 8 m wide, how deep is it?
4/3 m
An ellipse has foci at (±5, 0) and vertices at (±7, 0). What is the from its center to one endpoint of the minor axis?
√24
The vertices of a hyperbola are at (0, ±8) and its foci are at (0, ±10). Find b².
36