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Questions and Answers
A circle can be represented by the equation: (x - ______)^2 + (y - k)^2 = r^2
A circle can be represented by the equation: (x - ______)^2 + (y - k)^2 = r^2
h
To find the ______ and radius from the equation, follow these steps:
To find the ______ and radius from the equation, follow these steps:
center
Identify the values of h
and k
from the equation, which represent the ______ (h, k)
Identify the values of h
and k
from the equation, which represent the ______ (h, k)
center
Identify the value of r
from the equation, which represents the ______
Identify the value of r
from the equation, which represents the ______
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The ______ of the circle is the point (h, k)
in the equation (x - h)^2 + (y - k)^2 = r^2
The ______ of the circle is the point (h, k)
in the equation (x - h)^2 + (y - k)^2 = r^2
Signup and view all the answers
The ______ of the circle is the value of r
in the equation (x - h)^2 + (y - k)^2 = r^2
The ______ of the circle is the value of r
in the equation (x - h)^2 + (y - k)^2 = r^2
Signup and view all the answers
Study Notes
Circle Center and Radius from Equation
Circle Equation
- A circle can be represented by the equation:
(x - h)^2 + (y - k)^2 = r^2
- Where
(h, k)
is the center of the circle andr
is the radius
Finding the Center and Radius
- To find the center and radius from the equation, follow these steps:
- Write the equation in the standard form:
(x - h)^2 + (y - k)^2 = r^2
- Identify the values of
h
andk
from the equation, which represent the center(h, k)
- Identify the value of
r
from the equation, which represents the radius
Examples
- Equation:
(x - 2)^2 + (y - 3)^2 = 16
- Center:
(2, 3)
- Radius:
4
(sincer^2 = 16
,r = √16 = 4
)
- Center:
- Equation:
(x + 1)^2 + (y - 2)^2 = 25
- Center:
(-1, 2)
- Radius:
5
(sincer^2 = 25
,r = √25 = 5
)
- Center:
Key Concepts
- The center of the circle is the point
(h, k)
in the equation(x - h)^2 + (y - k)^2 = r^2
- The radius of the circle is the value of
r
in the equation(x - h)^2 + (y - k)^2 = r^2
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Description
Find the center and radius of a circle from its equation in standard form. Learn how to identify the values of h, k, and r from the equation and calculate the radius.