Question

Using the given information, write the equation of the circle.

1. Center: (-3, 4), Radius: 7

2. Center: (-9, 0), Diameter: 20

3. Center: (-7, -1), Diameter: 9

4. Center: (12, 5), Radius: Square root of 89

Answer 1

To write the equation of a circle, use the formula (x - h)^2 + (y - k)^2 = r^2. Substituting the given values of center and radius, we can find the equations of the circles.

Step-by-step explanation:

The equation of a circle in a Cartesian coordinate system is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Here are the circle equations for the provided centers and radius/diameter values:

• Center: (-3, 4), Radius: 7
  The equation is (x + 3)² + (y - 4)² = 49.

• Center: (-9, 0), Diameter: 20, Radius: 10
  The equation is (x + 9)² + y² = 100.

• Center: (-7, -1), Diameter: 9, Radius: 4.5
  The equation is (x + 7)² + (y + 1)² = 20.25.

• Center: (12, 5), Radius: √89
  The equation is (x - 12)² + (y - 5)² = 89.