ACT Prep: Circles & Parabolas

In the standard (x.y) coordinate plane, a circle has a center (-7,13) and a radius 9 coordinate units. Which of the following equations describes this circle?

• (x + 7)² + (y - 13)² = 9

• (x - 7)² + (y + 13)² = 9

• (x - 7)² - (y + 13)² = 9

• (x - 7)² + (y - 13)² = 81

• (x + 7)² + (y - 13)² = 81

What are the coordinates of the center of the circle with a radius of 1 and whose equation is x² + 10x + y² - 8y + 40 = 0 in the standard (x,y) coordinate plane?

• (-5,-4)

• (-5,4)

• (4,-5)

• (5,-4)

• (5,4)

Which of the following equations represents a circle in the standard (x,y) coordinate plane with its center at (-5,6) and a radius of 3 units?

• (x - 5)² + (y - 6)² = 9

• (x - 5)² + (y + 6)² = 9

• (x+ 5)² + (y - 6)² = 9

• (x - 5)² + (y + 6)² = 3

• (x + 5)² + (y - 6)² = 3

What are the coordinates of the center of a particular circle which has the equation x² + (y - 7)² = 13, and what is its radius, in coordinate units?

CENTER RADIUS

• (0, -7) & √13

• (0, -7) & 6.5

• (0, 7) & √13

• (0, 7) & 6.5

• (0, 7) & 13

A particular circle in the standard (x,y) coordinate plane intersects the y-axis at (0, 2) and (0, -14). The radius of the circle is 10 coordinate units. Which of the following could be the center of the circle?

I. (6, -6)

II. (0, -6)

III. (-6, -6)

• I only

• II only

• III only

• I and III only

• I, II, & III

What value of k gives the minimum value for p in the equation p = -5k + k² ?

• 2

• 5/2

• 15/4

• 5

• 15/2

In the standard (x,y) coordinate plane, a particular circle has center (9, 4) and is tangent to the y-axis. The point (x, y) lies on the circle if and only if x and y satisfy which of the equations below?

• (x + 9)² + (y + 4)² = 81

• (x + 9)² + (y + 4)² = 16

• (x + 9)² + (y + 4)² = 9

• (x - 9)² + (y - 4)² = 81

• (x - 9)² + (y - 4)² = 16

A particular circle in the standard (x,y) coordinate plane is centered at the origin and lies tangent to the line x = -5. What is the radius of this circle?

• 5

• 10

• √5

• 5 √2

• 5 √3

The graph of the equation x² /25 + y² /49 = 1 has a y-intercept at which of the following points?

• (0, 49)

• (0, 25)

• (0, 10)

• (0, 7)

• (0, 5)

The equation (x - 3)² + (y - 5)² = 29 describes a circle which intersects the x-axis at two points, one of which is (1, 0). What is the other point at which this circle intersects the x-axis?

• (-5, 0)

• (-1, 0)

• (0, 1)

• (1, 0)

• (5, 0)