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
andrey2020 [161]
3 years ago
15

A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

Mathematics
1 answer:
mario62 [17]3 years ago
3 0

Answer:

(x-7)^2+(y-5)^2=1

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

<u>Center of the circle:</u>

  • The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)

(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)

(x_m, y_m) = (7,5)

This is the center coordinate of our circle.

<u>Radius: </u>

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}

r = \sqrt{(6-7)^2+(5-5)^2}

r = \sqrt{1^2}

r = 1

<u>Equation of the circle: </u>

The equation is written as:

(x-a)^2+(y-b)^2=r^2

here, (a,b) are the center points of the circle

in our case this is (a,b)=(x_m,y_m)=(7,5)

and r = 1

(x-7)^2+(y-5)^2=1^2

(x-7)^2+(y-5)^2=1

This is the equation of the circle!

You might be interested in
What is the prime number 14 13 21 33
kvv77 [185]

Answer:

13 is the prime number

Step-by-step explanation:

Nothing can multiply to produce 13

8 0
3 years ago
Exact length of line segment xy
netineya [11]
length=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
4 0
3 years ago
The value of a dirt bike decreases by 20% each year. If you purchased this dirt bike today for $500, to the nearest dollar how m
jeka94
The value of the bike after a year becomes only 80% of the value a year ago. In this given, the initial amount $500 should be multiplied by 80% 5 times. The answer would be $163.84. Thus, after 5 years the dirt bike would only be $163.84. 
5 0
3 years ago
Read 2 more answers
Find the missing side of the triangle shown below, if the perimeter is 79.6.
astraxan [27]

Answer:

There is no picture

Step-by-step explanation:

7 0
2 years ago
How many times greater is 8 x 10^-2 than 2x10^-6
umka21 [38]

Answer:

40,000

Step-by-step explanation:

You want to start with the exponent and then multiply afterward in both of the equations.

8 x 10^-2:

10^-2 = 0.01

0.01 x 8 = 0.08

2 x 10^-6:

10^-6 = 0.000001

0.000001 x 2 = 0.000002

Obviously, you can see the relationship between 8 and 2 in the division.  Now, you just divide 0.08 by 0.000002 and you get 40,000.

4 0
1 year ago
Other questions:
  • Using traditional methods it takes 107 hours to receive an advanced flying license. A new training technique using Computer Aide
    6·1 answer
  • Write 9 minutes less than Chang’s time in algebraic expression
    13·1 answer
  • What is the factored form of 6x2 + 11x – 10?<br><br> (2x +<br> )(<br> x – <br> )
    10·1 answer
  • Three friends won $600 for winning a relay race. June ran 1/3 of the relay. Al ran 3/8 of the relay. Marcus ran 1/24 of the rela
    14·2 answers
  • Please Help Me!!!!<br> Max Points
    11·2 answers
  • When Kenneth woke up the temperature was
    12·2 answers
  • Maria tiene hielo en su refrigerador a 7c en cierto momento saco la cubeta del congelador y olvido guardarla nuevamente luego de
    6·1 answer
  • Please answer both questions, thanks!
    10·2 answers
  • The sum of twice a number and half the number is 10.<br><br><br>help pls :"​
    8·1 answer
  • For each of the number lines, write an absolute value equation that has the following solution set. 26 and m
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!