6 Questions
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:
center
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 ______
radius
The ______ of the circle is the point (h, k) in the equation (x - h)^2 + (y - k)^2 = r^2
center
The ______ of the circle is the value of r in the equation (x - h)^2 + (y - k)^2 = r^2
radius
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 andris 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
handkfrom the equation, which represent the center(h, k) - Identify the value of
rfrom 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
rin the equation(x - h)^2 + (y - k)^2 = r^2
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.
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