https://file.aiquickdraw.com/mathbot/file/1726151659459ydshkch2.jpg

The problem describes a radio station located at the coordinate \((4, 3)\) and having a maximum broadcasting range of 5 km. The task is to find the equation of a circle representing the maximum broadcasting range.

The general equation of a circle is:

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

where \((h, k)\) represents the center of the circle, and \(r\) is the radius.

For this problem:
- The center of the circle is \((4, 3)\).
- The radius \(r\) is 5 km.

Substituting these values into the equation:

\[
(x - 4)^2 + (y - 3)^2 = 5^2
\]

Simplifying:

\[
(x - 4)^2 + (y - 3)^2 = 25
\]

Thus, the equation representing the maximum range of the radio station is:

\[
(x - 4)^2 + (y - 3)^2 = 25
\]

Would you like further details or have any questions? 

Here are 5 related questions:
1. How would the equation change if the station's location shifted to \((6, 2)\)?
2. What is the area covered by the broadcasting signal of the station?
3. If the radius were doubled, what would be the new equation of the circle?
4. How would you determine the distance from a point to the radio station's location?
5. How can you find if a point lies within the broadcasting range?

**Tip:** When working with circle equations, remember that the center and radius are the most crucial components for determining its shape and position.

Suatu stasiun radio dengan posisi koordinat (4, 3) memiliki jangkauan maksimum siaran sejauh 5 km. Persamaan lingkaran untuk menunjukkan jangkauan maksimum siaran radio tersebut adalah ....

Discover how to find the equation of a circle representing the maximum broadcasting range of a radio station located at (4, 3) with a radius of 5 km. This solution covers geometric concepts and the formula for a circle. Ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation