#### Math - 2017-18

# G.12 and *G.12 - Equation of a Circle

**G.12** The student, given the coordinates of the
center of a circle and a point on the circle, will **write **the equation of the
circle.

G.12The student willsolveproblems involving equations of circles.

**Bloom's Level:** Analyze

*Adopted: 2009*

### BIG IDEAS

- I can determine the percentage of corn fields being watered
by circular irrigation sprinklers, how many miles a tire can travel before
wearing off its tread, and the best spot for a soccer player to stand on the
sideline to make a goal.

- I will
remember that when given the general form of a circle equation I can easily convert it to center-radius formby
completing the square.

### UNDERSTANDING THE STANDARD

- A circle is a locus of points equidistant from a
given point, the center.
- Standard form for the equation of a circle is (
*x - h*)^{2}+ (*y - k*)^{2}=*r*^{2}, where the coordinates of the center of the circle are (*h,k*) and*r*is the length of the radius. - The circle is a conic section.

· A circle is a locus of points equidistant from a given point, the center.

· The distance between any point on the circle and the center is the length of the radius.

·
Standard
form for the equation of a circle is (*x*
– *h*)^{2} + (*y* – *k*)^{2}
= *r*^{2}, where the
coordinates of the center of the circle are (*h*, *k*) and *r* is the length of the radius.

·
The equation
of a circle gives the coordinates of every point, (*x*, *y*), on the
circle.

· The midpoint formula and distance formula are important when determining the equation of a circle.

· The equation of a circle with a given center and radius can be derived using the Pythagorean Theorem.

· The midpoint of the diameter is the center of the circle.

### ESSENTIALS

G.12_{1}
**Identify** the center, radius, and diameter of a circle from a given
standard equation.

G.12_{4} Given
the equation of a circle in standard form, **identify**
the coordinates of the center and **find**
the radius of the circle.

·
G.12_{1} Given a graph or the equation of a circle in
standard form, **identify** the
coordinates of the center of the circle.

·
G.12_{3} Given a graph or the equation of a circle in
standard form, **identify** the length
of the radius or diameter of the circle.

G.12_{2}
**Use** the distance formula to **find**
the radius of a circle.

·
G.12_{5} Given the coordinates of the center and the
coordinates of a point on the circle, **determine**
the length of the radius or diameter of the circle.

G.12_{3}
Given the coordinates of the center
and radius of the circle, **identify** a
point on the circle.

·
G.12_{6} Given the coordinates of the center and
length of the radius of a circle, **identify**
the coordinates of a point(s) on the circle.

G.12_{5}
Given the coordinates of the endpoints
of a diameter, **find** the equation of
the circle.

·
G.12_{4} Given the coordinates of the endpoints of the
diameter of a circle, **determine** the
length of the radius or diameter of the circle.

·
G.12_{2} Given the coordinates of the endpoints of a
diameter of a circle, **determine** the
coordinates of the center of the circle.

G.12_{6}
Given the coordinates of the center
and a point on the circle, **find** the
equation of the circle.

·
G.12_{7} **Determine**
the equation of a circle given:

a graph of a circle with a center with coordinates that are integers;

coordinates of the center and a point on the circle;

coordinates of the center and the length of the radius or diameter; or

coordinates of the endpoints of a diameter.

G.12_{7} **Recognize** that the equation of a circle
of given center and radius is derived using the Pythagorean Theorem.

### KEY VOCABULARY

circle,
center, point, equation, equation of circle, (x,y), (h,k), radius, diameter,
standard equation, distance formula, locus of points, coordinates, identify,
endpoint, Pythagorean Theorem, equidistant, conic section

*Updated: Feb 22, 2018*