What do I do to graph:

(x-2)^2+(y-4)^2=9

The standard form equation of a circle :

( x - h ) ^ 2 + ( y - k ) ^ 2 = r ^ 2

h are the x coordinates of the center of the circle

k are the y coordinates of the center of the circle

r = radius

In this case:

x coordinate of the center = 2

y coordinate of the center = 4

r = sqrt ( 9 ) = 3

Draw coordinate system , put driver in point ( x = 2 , y = 4 ) and drive circle with radius = 3

y coordinate

they are right

To graph the equation (x-2)^2 + (y-4)^2 = 9, which represents a circle, we can use the following steps:

1. Start by recognizing that the equation is in the standard form for a circle, which is (x - h)^2 + (y - k)^2 = r^2. In this equation, (h, k) represents the center of the circle, and r represents the radius.

2. Identify the values of h, k, and r in the given equation. Comparing the given equation (x-2)^2 + (y-4)^2 = 9 with the standard form, we see that h = 2, k = 4, and r^2 = 9. Taking the square root of r^2, we find that the radius r = 3.

3. Plot the center point (h, k) on the coordinate plane. In this case, the center is at (2, 4). Mark this point on the graph.

4. Use the radius to draw the circle around the center point. The radius is 3 units, so starting from the center (2, 4), plot points that are 3 units away in all directions. Connect these points to create a circle.

5. Verify that the equation matches the graph you have drawn. Take any point on the circle and substitute its x and y coordinates into the equation. If the equation holds true for that point, then the graph is correct.

In summary, to graph the equation (x-2)^2 + (y-4)^2 = 9:
- Plot the center point (2, 4).
- Use the radius of 3 units to draw a circle around the center point.
- Verify that any point on the graph satisfies the equation by substituting its coordinates into the equation.