The endpoints of a diameter of a circle are ( 3 , 9 ) and ( 3 , - 3 ). Find the equation of the circle.

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle. The given end points of the diameter are  

(

3

,

−

1

)

and  

(

9

,

1

)

. The center point of the circle is the center of the diameter, which is the midpoint between  

(

3

,

−

1

)

and  

(

9

,

1

)

. In this case the midpoint is  

(

6

,

0

)

.

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(

6

,

0

)

Find the radius  

r

for the circle. The radius is any line segment from the center of the circle to any point on its circumference. In this case,  

r

is the distance between  

(

6

,

0

)

and  

(

3

,

−

1

)

.

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r

=

√

10

(

x

−

h

)

2

+

(

y

−

k

)

2

=

r

2

is the equation form for a circle with  

r

radius and  

(

h

,

k

)

as the center point. In this case,  

r

=

√

10

and the center point is  

(

6

,

0

)

. The equation for the circle is  

(

x

−

(

6

)

)

2

+

(

y

−

(

0

)

)

2

=

(

√

10

)

2

.

(

x

−

(

6

)

)

2

+

(

y

−

(

0

)

)

2

=

(

√

10

)

2

The circle equation is  

(

x

−

6

)

2

+

(

y

−

0

)

2

=

10

.

(

x

−

6

)

2

+

(

y

−

0

)

2

=

10

Simplify the circle equation.

(

x

−

6

)

2

+

y

2

=

10

image of graph

Step-by-step explanation:

(x-3)^2 + (y-3)^2 = 36

Step-by-step explanation:

Given endpoints of a diameter of a circle are ( 3 , 9 ) and ( 3 , - 3 )

(3+3)/2 = 3, (9-3)/2 = 3 and (9-(-3))/2 = 6

So center of circle is at (3, 3) and radius = 6

The general equation of circle is given by (x-a)^2 + (y-b)^2 = r^2

(x-3)^2 + (y-3)^2 = 6^2

(x-3)^2 + (y-3)^2 = 36