a circle has a radius of 98 squared units and is centered at (5.9,6.7) 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 \((h, k) = (5.9, 6.7)\)
- Radius \(r = 98\) units

Substituting these values into the equation:

\[
(x - 5.9)^2 + (y - 6.7)^2 = 98^2
\]

Simplifying \(98^2\):

\[
98^2 = 9604
\]

So, the equation of the circle is:

\[
(x - 5.9)^2 + (y - 6.7)^2 = 9604
\]

Would you like further details or have any questions?

Here are some related questions:
1. How would you derive the radius from the equation of a circle?
2. What is the area of the circle with the given radius?
3. How do you determine the coordinates of the center if only the equation is given?
4. What happens to the equation if the circle's radius is increased by 50%?
5. How do you determine the distance between the center and any given point on the circle?
6. How do you find the length of the chord of the circle?
7. What would the equation look like if the center were shifted to \((0, 0)\)?
8. What is the equation of a circle that passes through the origin with the same radius?

**Tip:** Always double-check your calculations when working with large squared values to avoid errors in the final equation.

Learn how to write the equation of a circle with a radius of 98 units and centered at (5.9, 6.7). This problem covers the formula for the equation of a circle, center-radius form, and calculations involving squared values. Suitable for high school students studying geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation