i need to graph this equation
(x-3)^2+(y+5)^2=9
this has me totally confused.
What is the standard form for the equation of a circle? Consult your text.
Your school subject is NOT college; it's MATH.
I can help you step-by-step to graph the equation (x-3)^2 + (y+5)^2 = 9:
Step 1: Identify the center of the circle
The equation is in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle. In this case, the center is (3, -5).
Step 2: Determine the radius of the circle
In the equation, r^2 represents the radius squared. In this case, the radius is 3 (since 9 = 3^2).
Step 3: Plot the center of the circle
On a coordinate plane, plot the point (3, -5).
Step 4: Draw the circle
Using the center and radius, draw a circle on the graph. The radius should be 3 units, and the center should be the point (3, -5).
Step 5: Determine the intercepts
Find the x and y-intercepts of the equation. To find the x-intercepts, let y = 0 and solve for x. To find the y-intercepts, let x = 0 and solve for y.
For x-intercept: (x - 3)^2 + (0 + 5)^2 = 9
(x - 3)^2 + 25 = 9
(x - 3)^2 = -16 (no x-intercepts, since this equation has no real solution)
For y-intercept: (0 - 3)^2 + (y + 5)^2 = 9
9 + (y + 5)^2 = 9
(y + 5)^2 = 0
y + 5 = 0
y = -5
The y-intercept is -5. Plot the point (0, -5) on the graph.
Step 6: Connect the intercepts
Draw a line connecting the x-intercepts (if any) and the y-intercept.
Here's a summary of the steps:
1. Plot the center (3, -5).
2. Draw a circle with a radius of 3 units around the center.
3. Plot the y-intercept at (0, -5).
4. Connect the intercepts and any other relevant points on the circle.
I hope this clarifies the process for graphing the equation for you!
To graph the equation (x - 3)^2 + (y + 5)^2 = 9, you can follow these steps:
Step 1: Understand the equation:
The equation represents a circle with its center at the point (3, -5) and a radius of 3. This is because the equation is in standard form: (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius.
Step 2: Plot the center of the circle:
The center of the circle is (3, -5). Mark this point on your graph.
Step 3: Plot the radius:
The radius of the circle is 3. Starting from the center point, you can draw a circle with a radius of 3 units in all directions. This means you can plot points on the circle that are 3 units away from the center.
Step 4: Draw the circle:
Using the center as a starting point, plot several points around the circle with a radius of 3 units. Then, connect these points to form a smooth curve. This curve represents the graph of the equation.
Step 5: Add any additional details:
If necessary, you can add a scale to your graph and label the x-axis and y-axis.
By following these steps, you should be able to graph the equation (x - 3)^2 + (y + 5)^2 = 9 accurately.