a circle has a radius of 37 squared units and is centered at (1.3,-3.5) write the equation of this circle

The general equation of a circle with a center at \((h, k)\) and a radius \(r\) is given by:

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

Given:
- Center \((h, k) = (1.3, -3.5)\)
- Radius \(r = 37\) units

Substituting these values into the equation:

\[
(x - 1.3)^2 + (y + 3.5)^2 = 37^2
\]

Simplifying \(37^2\):

\[
37^2 = 1369
\]

So, the equation of the circle is:

\[
(x - 1.3)^2 + (y + 3.5)^2 = 1369
\]

Would you like further details or have any questions?

Here are some related questions:
1. How would the equation change if the radius were doubled?
2. What is the area of the circle described by this equation?
3. How do you find the diameter of the circle?
4. What is the circumference of the circle?
5. How does changing the center affect the equation of a circle?
6. What are the coordinates of the center and the radius if the equation is given in the standard form?
7. How can you determine if a point lies inside, on, or outside the circle?
8. What would be the equation if the circle were shifted 5 units to the right?

**Tip:** To verify if a point lies on a circle, substitute the point's coordinates into the circle's equation.

Learn how to write the equation of a circle with a radius of 37 units and centered at (1.3, -3.5). This problem covers the equation of a circle formula and its application to specific geometric coordinates.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation