equation of a circle

Question

3. The equation of a circle is (x + 3)2 + (y + 5)2 = 8. Determine the coordinates of the center of the circle.

A) Center (-3, -5)

B) Center (3, 5)

C) Center (-5, -3)

D) Center (5, 3)

4. The equation of a circle is (x + 7)2 + (y + 2)2 = 49. Determine the length of the diameter.

A) 7 B) 49 C) 9 D) 14

5. Earthquakes release seismic waves that occur in concentric circles from the epicenter of the earthquake. Suppose a seismograph station determines the epicenter of an earthquake is located 9 kilometers from the station. If the epicenter is located at the origin, write the equation for the circular wave that passes through the station.

A) x2 + y2 = 81 B) x2 + y2 = 9 C) (x - 9)2 + (y - 9)2 = 0 D) (x + 9)2 + (y + 9)2 = 0

Answer 1

The standard  form of circle equation is ---> (1)

Where

3)

Compare it to circle equation (1).

Option A  is correct choice.

4) 

Compare it to circle equation (1).

Option D  is correct choice.

5)  Assume that the location of the station at (0,0) on a coordinate grid.

The epicenter could be any place on a circle which has it's center (0,0) and radius(r) is 9.

Substitute the center and r  in equation (1).

Option A  is correct choice.