Geometry help?? 10 POINTS?

Question

 For the circle with equation (x – 2)2 + (y + 3)2 = 9, answer each question: 
a) What are the coordinates of the center?
b) What are the radius and diameter of the circle?
c) Graph the circle.

Answer 1

a.The circle equation is (x – 2)2 + (y + 3)2 = 9

genral formula of circle equation is (x -h)^2 + (y-k)^2 = r^2

( x - 2 )^2 + ( y - (-3) )^2 = 3^2

center (h,k) = ( 2, -3 ).

Answer 2

b.The circle equation is (x – 2)2 + (y + 3)2 = 9

genral formula of circle equation is (x -h)^2 + (y-k)^2 = r^2

( x - 2 )^2 + ( y - (-3) )^2 = 3^2

center (h,k) = ( 2, -3 ).and radius (r) = 3.

The diameter of the circle is d = 2r ⇒d = 2(3) ⇒ d = 6

Answer 3

c) To graph of the circle.

Answer 4

a) The circle equation is (x - 2)² + (y + 3)² = 9

(x - 2)² + (y - (-3))² = 3²

Compare it to standard form of a circle equation is

Where center is (h ,k ) and radius of circle is r .

center of circle is (2,-3)

b) Radius of circle r = 3

Diameter = 2r = 6

c) To graph the circle we need few more coordinates.

Center at (2,-3) and r = 2, So we plot

Up (2, -3+3) = (2, 0)

Down (2, -3-3) = (2, -6)

Left (2-3, -3) = (-1, -3)

Right (2+3, -3) = (5, -3)

Graph

1. draw the coordinate plane.

2. Plot the center at (2,-3).

3. Plot 4 points " radius" away from the center in the up, down, left and right direction.

4. Sketch the circle.