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
Fed [463]
3 years ago
14

Find an equation of the circle whose diameter has endpoints , 6−2 and , −4−4 .

Mathematics
1 answer:
MrRissso [65]3 years ago
4 0
If you need just the answer, it's in bold at the bottom. Otherwise, the process for how I got there is below. 

In order to find the equation, we first find the midpoint. This will give us the center of the two endpoints. Then, we do the distance formula to find how many units there are between the endpoints and cut it in half to find the radius. After, we plug in the new information into the equation format of the circle. 

Midpoint = ( \frac{x_{1}+ x_{2} }{2},  \frac{ y_{1} + y_{2} }{2} )

So plug in the ordered pairs given to get: 

Midpoint = ( \frac{6-4}{2},  \frac{-2-4}{2})
Midpoint = ( \frac{2}{2},  \frac{-6}{2})
Midpoint = (1, - 3)

This is your center.

Now for the distance between the endpoints. 

Distance = √((X₂ - X₁)² + (Y₂ - Y₁)²)
Distance = √((-4 - 6)² + (-4 - (-2))²)
Distance = √((- 10)² + (- 2)²)
Distance = √(100 + 4)
Distance = √104 which simplifies to 2√26

So the distance between the two endpoints (the diameter) is 2√26 units long. We divide this by 2 and get the measurement of the radius. The radius is √26 units long. 

Now we plug in to the equation of a circle:

(x - h)² + (y - k)² = r² 

The center of the circle is represented by the ordered pair (h, k) and the radius is represented by r. 

So your equation becomes:
(x - 1)² + (y + 3)² = (√26)²

Which simplifies to your final answer:

(x - 1)² + (y + 3)² = 26

You might be interested in
Which set of numbers represents a Pythagorean triple
Anuta_ua [19.1K]

Answer:

27,36,45

Step-by-step explanation:

Pythagorean theorem

a^{2} +b^{2} =c^{2}

6^{2}+ 9^{2}\\ =117\\\neq 12^{2}

7^{2}+ 10^{2}\\ =149\\\neq 12^{2}

16^{2}+ 18^{2}\\ =580\\\neq 25^{2}

27^{2}+ 36^{2}\\ =2025\\= 45^{2}

3 0
3 years ago
Find the least common multiple of 18, 24, 42
Lana71 [14]

Answer: 504. Multiple for : 18, 24 and 42. Factorize of the above numbers : 18 = 2 • 32 24 = 23 • 3. 42 = 2 • 3 • 7

5 0
3 years ago
Solve x. 10(2x - 4) = 100x
mr_godi [17]

Answer:

x=1/2

Step-by-step explanation:

Distribute the 10. it will be 20x-40=100x. Subtract 20x from both sides. it will be 40=80x. Divide by 80 to leave the x by itself. x=40/80...in simplify form....its 1/2

3 0
3 years ago
Please help find x!!
VMariaS [17]

Answer:

X= 360- (180+35)

X= 145

Step-by-step explanation:

since angle at a point is same as angle in a circle =360°

And we've being given two values out of three that makes up the point. so we subtract the sum of the two values from the size of angle at a point

4 0
2 years ago
PLEASE HELP! i have by the end of the day to turn this in. PLEASE DONT GUESS
SVEN [57.7K]

Answer:

122

Step-by-step explanation:

x = 180-(180-50-72) = 180-(130 - 72) = 180 - 130 + 72 = 50 + 72 = 122

6 0
3 years ago
Read 2 more answers
Other questions:
  • The area of a rectangle is 28square miles. The length is 7 miles.
    6·1 answer
  • Joanna bought pounds of apples, of a pound of strawberries, of a pound of grapes, pounds of oranges, and pounds of pears. How ma
    14·1 answer
  • Please help me....im literally desperate! 25pts and BRAINLIEST!!!
    15·1 answer
  • Use the graph to answer #3-6.<br> U WILL B MARKED BRANLIEST ASAP
    15·1 answer
  • HELP I NEED HELP ASAP
    14·2 answers
  • T-test Statistics
    10·1 answer
  • Please help!!!!! Due Today in a couple hours!!!!!
    11·2 answers
  • What is the diameter of a circle with circumference<br> C= 191 ? Leave answers in exact form.
    10·1 answer
  • A food company distributes its tomato soup in two cans of different sizes. For the larger can, both the diameter and the height
    7·1 answer
  • What are the characteristics of a pie chart?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!