Graphing A Circle help?

Question

1) Graph the circle (x – 4)^2 + (y – 2)^2 = 25.  Label the center and at least four points on the circle

2)  Graph the circle (x + 2)^2 + (y + 1)^2 = 32.  Label the center and at least four points on the circle.

3)  Graph the circle x^2 + (y + 2)^2 = 9.  Label the center and at least four points on the circle.

4)  Graph the circle with center at (4, 0) and radius 3.  Label the center and at least four points on the circle.  Write the equation of the circle.

Equation of circle:
5)  Graph the circle with center at (-4, 2) and radius 5.  Label the center and at least four points on the circle.  Write the equation of the circle.

Equation of circle:
6)  Graph the circle with center at (-1, 2) and diameter 12.  Label the center and at least four points on the circle.  Write the equation of the circle.

Equation of circle:

7)  Graph the circle with center at (3, -2), which also passes through the point (0, 2).  Label the center and at least four points on the circle.  Write the equation of the circle.

Equation of circle:
8)  Graph the circle with center at (-1, -2), which also passes through the point (0, 2).  Label the center and at least four points on the circle.  Write the equation of the circle.

Equation of circle:

9)  Challenge:  Graph the equation with a diameter that has endpoints at (-3, 4) and (5, -2).  Label the center and at least four points on the circle.  Write the equation of the circle.

Equation of circle:
10) Challenge:  Graph the equation with a diameter that has endpoints at (-2, -2) and (4, 2).  Label the center and at least four points on the circle.  Write the equation of the circle.

Answer 1

(2)

Step 1:

The circle equation is .

The standard form of circle equation is , where is the center of the circle and is radius.

Compare the circle equation with standard form.

Here and .

The circle equation is .

Solve the circle equation for .

.

Construct a table for different values of .

Step 2:

Graph the circle equation is .

Plot the center and and points.

Solution:

Graph of the circle :

.

Answer 2

1)

Step 1:

Equation of the circle is .

Standard form of the circle is .

Here center .

Compare the circle equation with the standard form.

Center and .

Consider

Solve for .

Construct a table for different values of .

Step 2:

Graph :

Plot the center  and radius .

Plot the points obtained in the table.

Connect those points with a smooth curve.

Graph the circle .

Solution:

Graph of the circle  is 

Answer 3

(3)

Step1:

The circle equation is .

The standard form of circle equation is , where is the center of the circle and is radius.

Compare the circle equation with standard form.

Here and .

The circle equation is .

Solve the circle equation for .

.

Step 2:

Graph the circle equation is .

Plot the points obtained in the table.

Plot the center and and points.

Solution:

Graph of the circle :

Answer 4

(4)

Step 1:

The center of the cirle is and the radius is .

The standard form of circle equation is , where is the center of the circle and is radius.

Substitute and in standard form of circle equation.

.

The circle equation is .

Solve the circle equation for .

.

Construct a table for different values of .

Step 2:

Plot the center and .

plot the points obtained in the table.

Connect those points with smooth curve.

Graph the circle  .

Solution:

Graph of the circle :

Answer 5

(5)

Step 1:

The center of the cirle is and the radius is .

The standard form of circle equation is , where is the center of the circle and is radius.

Substitute and in standard form of circle equation.

The circle equation is .

Solve the circle equation for .

.

Construct a table for different values of .

Step 2:

Plot the center and .

plot the points obtained in the table.

Connect those points with smooth curve.

Graph the circle .

Solution:

Graph of the circle :

Answer 6

(6)

Step1:

The center of the cirle is and the diameter is .

Radius of the circle is .

Substitute in the .

.

The standard form of circle equation is , where is the center of the circle and is radius.

Substitute and in the standard form of the circle equation.

Solve the circle equation for .

.

Step 2:

Plot the center and .

plot the points obtained in the table.

Connect those points with smooth curve.

Graph the circle .

Solution:

Graph of the circle :

Answer 7

(7)

Step 1:

The center of the cirle is .

The circle passes through the point is .

The distance from center to any point on the circle is its radius.

.

The radius of the circle is .

Step 2:

The standard form of circle equation is , where is the center of the circle and is radius.

Substitute center and in standard form of circle equation.

The circle equation is .

Solve the circle equation for .

.

Construct a table for different values of .

Step 3:

Plot the center and .

Plot the points obtained in the table.

Connect those points with smooth curve.

Solution:

Graph of the circle is

The circle equation is .

Answer 8

(8)

Step 1:

The center of the cirle is .

The circle passes through the point .

The distance from center to any point on the circle is its radius.

 

.

The radius of the circle is .

Step 2:

The standard form of circle equation is , where  is the center of the circle and  is radius.

Substitute  and  in standard form of circle equation.

The circle equation is .

Solve the circle equation for .

.

Construct a table for different values of .

Step 3:

Plot the center  and .

Plot the points obtained in the table.

Connect those points with smooth curve.

Graph the circle .

Solution:

Graph of the circle is

The circle equation is .

Answer 9

(9)

Step 1:

The end points of the circle diameter are and .

The disance between the two end points is the diameter of the circle.

.

The radius of the circle is .

The mid point of the two end points is the center of the circle.

.

The center of the cirle is .

Step 2:

The standard form of circle equation is , where is the center of the circle and is radius.

Substitute and in standard form of circle equation.

The circle equation is .

Solve the circle equation for .

.

Construct a table for different values of .

Step 3:

Plot the center and .

Plot the points obtained in the table.

Connect those points with smooth curve.

Graph the circle .

Solution:

Graph of the circle is

The equation of the circle is .

Answer 10

(10)

Step 1:

The end points of the circle diameter are and .

The disance between the two end points is the diameter of the circle.

.

The radius of the circle is .

The mid point of the two end points is the center of the circle.

The center of the cirle is .

Step 2:

The standard form of circle equation is , where is the center of the circle and is radius.

Substitute and in standard form of circle equation.

The circle equation is .

Solve the circle equation for .

.

Construct a table for different values of .

Step 3:

Plot the center and .

Plot the points obtained in the table.

Connect those points with smooth curve.

Graph the circle .

Solution:

Graph of the circle is

The equation of the circle is .