Question

Write the standard equation for the circle that passes through the points (- 5, 0), (0, 4), and (2, 4).

Answer 1

Answer:

x

2

+

y

2

−

6

x

+

4

y

−

37

=

0

 

Explanation:

let's substitute each coordinate of all points in the general equation of the circle:

x

2

+

y

2

+

a

x

+

b

y

+

c

=

0

so that you have three equations with unknown variables a,b,c:

4

2

+

5

2

+

4

a

+

5

b

+

c

=

0

and

(

−

2

)

2

+

3

2

−

2

a

+

3

b

+

c

and

(

−

4

)

2

+

(

−

3

)

2

−

4

a

−

3

b

+

c

=

0

let's solve in a few steps:

4

a

+

5

b

+

c

+

41

=

0

and

−

2

a

+

3

b

+

c

+

13

=

0

and

−

4

a

−

3

b

+

c

+

25

=

0

c

=

−

4

a

−

5

b

−

41

and

(by substituting c)  

−

2

a

+

3

b

−

4

a

−

5

b

−

41

+

13

=

0

and

−

4

a

−

3

b

−

4

a

−

5

b

−

41

+

25

=

0

−

6

a

−

2

b

−

28

=

0

and

−

8

a

−

8

b

−

16

=

0

that is equivalent to:

3

a

+

b

+

14

=

0

and

a

+

b

+

2

=

0

By subtracting you obtain:

2

a

+

12

=

0

a

=

−

6

so, by substituting the obtained value of a:

−

6

+

b

+

2

=

0

b

=

4

so

c

=

−

4

(

−

6

)

−

5

(

4

)

−

41

=

24

−

20

−

41

=

−

37

The equation of the circle is:

x

2

+

y

2

−

6

x

+

4

y

−

37

=

0

Step-by-step explanation: