Center: (10, -12) Point On Circle: (11, -11)

To find the equation of the circle given the center and a point on the circle, you can use the standard form of the equation of a circle:

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

Where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius.

### Step 1: Identify the center and point on the circle.
- Center: \((h, k) = (10, -12)\)
- Point on the circle: \((x_1, y_1) = (11, -11)\)

### Step 2: Calculate the radius \(r\).
The radius \(r\) is the distance between the center \((10, -12)\) and the point on the circle \((11, -11)\). You can calculate this using the distance formula:

\[
r = \sqrt{(x_1 - h)^2 + (y_1 - k)^2}
\]

Substituting the values:

\[
r = \sqrt{(11 - 10)^2 + (-11 + 12)^2}
\]

\[
r = \sqrt{1^2 + 1^2} = \sqrt{1 + 1} = \sqrt{2}
\]

### Step 3: Write the equation of the circle.
Now that we have the radius \(r = \sqrt{2}\), we can write the equation of the circle:

\[
(x - 10)^2 + (y + 12)^2 = 2
\]

This is the equation of the circle.

Would you like more details on any part of this solution or have any questions?

Here are some related questions you might find interesting:
1. How do you find the equation of a circle given two points on the circle?
2. What is the general form of a circle's equation?
3. How do you convert the equation of a circle from standard form to general form?
4. How do you find the center and radius of a circle given its equation?
5. How can you find the points of intersection between two circles?

**Tip:** The radius of a circle can always be found using the distance formula between the center and any point on the circle.

Find out how to derive the equation of a circle given the center at (10, -12) and a point on the circle at (11, -11). This problem involves using the distance formula to calculate the radius and applying the standard form of the equation of a circle. Ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation