Equations of Circles in the Coordinate Plane

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

• 4

• 2

• 3

• 16

What does the r in the standard equation stand for?

• r is the distance of the circle

  
  

• 
  r is the y coordinate of the center of the circle

• r is the radius of the circle

• 
  r is the x coordinate of the center of the circle

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)

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?

• (0, -7) & √13

• (0, -7) & 6.5

• (0, 7) & √13

• (0, 7) & 6.5

• (0, 7) & 13

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

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)

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

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

In an example from the second video in 10.3, the parametric equation x = 3cost, y = 3sint became...

• circle

• ellipse

• hyperbolas

• parabola