Write the standard equation for the circle that passes through the points: (-1, 2) (4, 2) (- 3, 4)

(

x

−

5

3

)

2

+

(

y

−

5

3

)

2

−

65

9

=

0

Explanation:

The circle's general equation is

C

→

(

x

−

x

0

)

2

+

(

y

−

y

0

)

2

−

r

2

=

0

This equation must be obeyed by the three points. Substituting  

{

x

,

y

}

for each point we have

⎧

⎪

⎪

⎨

⎪

⎪

⎩

2

x

0

+

x

2

0

−

4

y

0

+

y

2

0

+

5

−

r

2

=

0

−

6

x

0

+

x

2

0

−

8

y

0

+

y

2

0

+

25

−

r

2

=

0

−

4

x

0

+

x

2

0

+

2

y

0

+

y

2

0

+

5

−

r

2

=

0

Those equations are easily handled taking the difference between the first and the second, and the first and the third, obtaining

{

2

x

0

+

y

0

−

5

=

0

x

0

−

y

0

=

0

Solving for  

x

0

,

y

0

we obtain

{

x

0

=

5

3

,

y

0

=

5

3

}

r

is obtained putting those results in any of the equations already obtained

r

=

√

65

3

Step-by-step explanation:

answer

106 emergencies

step-by-step explanation: