Rachel Rosen 8-3
Study Guide: 9.3- Circles
Let’s start from the very beginning.
Circle basics:
- A circle is a continuous curve with no vertices or edges.
- Every point on a circle will be the same difference from a center point. This distance is called the radius.
- All circles have a diameter, which is the difference across the whole circle.
It is twice the value of the radius.
- The circumference is the distance around the edge of the circle. It is calculated by multiplying the diameter by pi, 3.141592….
- The area of the circle is calculated by squaring the radius and then multiplying it by pi.
What is the standard equation of a circle?
x^2+ y^2=r^2this equation is only for circles with its center on the origin.
As long as the radius is found, this equation can be graphed.
This is the graphed equation if x^2+y^2=4. The radius
is 2; 2^2=4.
Want to try a few?
Practice!
- What is the equation for this circle?
- Draw the graph for the equationx^2+y^2=25
- Draw the graph for the equationx^2+y^2=1
If the circle is not centered on the origin, it has been translated. The standard equation for a translated circle is
(x-h)^2+(y-k)^2=r^2.
(h,k)is the center.
The center of this circle is (0,2). It is only
Translated up, so there is no need for an H
value. The equation for this circle is
x^2+(y-2)^2=4.
More Practice!
Write the equations for these circles.
1.
2.
2.
- Draw the circle for the equation (x-3)^2+(y-1)^2=4
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Answers!
Practice #1:
- X^2+Y^2=16
3.
Practice #2:
- (x-2)^2+(y-3)^2=16
- (x-2)+(y-2)^2=16
3.
You are now an expert circle maker!!
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