Last updated on June 24th, 2025
A calculator is a tool designed to perform both basic arithmetic operations and advanced calculations, such as those involving geometry. It is especially helpful for completing mathematical school projects or exploring complex mathematical concepts. In this topic, we will discuss the Equation Of Circle Calculator.
The Equation Of Circle Calculator is a tool designed for determining the equation of a circle.
A circle is a two-dimensional shape where all points are equidistant from a central point.
The equation of a circle in a standard form is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
To determine the equation of a circle using the calculator, follow the steps below:
Step 1: Input: Enter the center coordinates (h, k) and the radius r.
Step 2: Click: Calculate Equation. By doing so, the inputs will be processed.
Step 3: You will see the equation of the circle in the output column.
Below are some tips to help you get the right result using the Equation Of Circle Calculator.
The equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Ensure the radius and coordinates are in the right units, like centimeters or meters.
When entering the center and radius, make sure the numbers are accurate. Small mistakes can lead to incorrect equations.
Calculators mostly help us with quick solutions. For calculating geometric problems, students must know the intricate features of a calculator. Given below are some common mistakes and solutions to tackle these mistakes.
Help Emily find the equation of a circle with center at (2, -3) and a radius of 5 cm.
The equation of the circle is (x - 2)² + (y + 3)² = 25.
To find the equation, we use the formula: (x - h)² + (y - k)² = r²
Here, the center (h, k) is (2, -3) and the radius r is 5.
Substitute these values into the formula: (x - 2)² + (y + 3)² = 5² = 25.
The center of a fountain is at (-4, 6) and it has a radius of 7 meters. What is the equation of the circle representing the fountain's boundary?
The equation is (x + 4)² + (y - 6)² = 49.
To find the equation, we use the formula: (x - h)² + (y - k)² = r²
Since the center (h, k) is (-4, 6) and radius r is 7,
we can find the equation as: (x + 4)² + (y - 6)² = 7² = 49.
Find the equation of a circle with a center at the origin and a radius of 10 units.
The equation is x² + y² = 100.
For a circle with a center at the origin (0,0), we use the formula (x - 0)² + (y - 0)² = r².
Substitute the radius r as 10: x² + y² = 10² = 100.
A circular garden has its center at (6, -8) with a radius of 12 feet. Find the circle's equation.
The equation of the circle is (x - 6)² + (y + 8)² = 144.
Using the formula (x - h)² + (y - k)² = r², with center (h, k) as (6, -8) and radius r as 12,
we get: (x - 6)² + (y + 8)² = 12² = 144.
Sarah's backyard pool is circular, with a center at (3, 5) and a radius of 8 meters. What is the equation of the pool's boundary?
The equation of the circle is (x - 3)² + (y - 5)² = 64.
The equation of the circle is found using the formula (x - h)² + (y - k)² = r².
With center (h, k) as (3, 5) and radius r as 8, substitute these values: (x - 3)² + (y - 5)² = 8² = 64.
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
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