1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Igoryamba
3 years ago
14

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

Mathematics
1 answer:
solong [7]3 years ago
8 0

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:

You might be interested in
Find the surface area
Nikitich [7]
The answer to the question is that the surface area is 48
3 0
2 years ago
Gina has been present at school for 40 of the first 45 days of the school year. The school year is 180 days long. If Gina contin
guapka [62]

The answer is going to be 160.

6 0
3 years ago
Read 2 more answers
What is the volume of the following cylinder in cubic feet?
Salsk061 [2.6K]
5089.38 is the volume
5 0
2 years ago
If b = 5, what is b to the square root of 3
liubo4ka [24]
Is 125 because u need to take the 5 and add 3 on the top

6 0
3 years ago
Each section of a running trail is 3/4 mile. The trail has 3 sections. Which expression tells how many miles long the entire tra
allsm [11]
3/4*3=2.25 miles long trail
Have a great day
8 0
2 years ago
Other questions:
  • Damon is 7 years older than his brother Mark. The sum of Damon and Mark's age is 29.
    10·1 answer
  • Please help asaaappp!!!!!!!!!!!
    8·2 answers
  • 60 min is 20 percent of blank min
    12·1 answer
  • Weekly wages at a certain factory are
    15·1 answer
  • Can someone help me with this worksheet? I'm trying to check my daughter's work and I'm not sure how to do this. Showing the wor
    11·1 answer
  • Please help me thanks
    10·1 answer
  • (a) Michael bought 19 pounds of sugar for $8. How many dollars did he pay per pound
    6·1 answer
  • Write an equation, in slope-intercept form(y = mx + b) that models the total cost of the rental over time.
    15·2 answers
  • 6. this solid has curved sides. all cross sections parallel to the base are squares measuring 3 units on each side. the height f
    6·1 answer
  • The graph of which equation is shown below?<br>Please answer quickly!!!​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!