The points (1, 4) and (−3, 2) are the endpoints of a diameter of a circle. What is the equation of the circle?
Answers
Answer:
Step by step
Step-by-step explanation:
Since we have the endpoints of the diameter, the midpoint coordinates of the line segment joining them gives the centre of the circle.
That is, centre (a,b) = ( [1+(-3)]/2, [4+2]/2) = (-1,3)
Distance between the given points give the diameter and half of that is the radius length.
So, radius r = (1/2)* sqrt ( [1-(-3)]^2 + [4–2]^2) = sqrt(5)
Thus equation required is: (x-a)^2 + (y-b)^2 = r^2
So, (x+1)^2 + (y-3)^2 = 5
The equation of the circle is (x + 1)² + (y - 3)² = 5
How to determine the circle equation?The endpoints of the diameter are given as:
(1, 4) and (−3, 2)
Start by calculating the midpoint using:
Midpoint = 0.5 * (x₁ + x₂, y₁ + y₂)
So, we have:
Midpoint = 0.5 * (1 - 3, 4 + 2)
Evaluate
Midpoint = (-1, 3)
So, the center (a,b) of the circle is:
(a,b) = (-1,3)
Calculate the length of the diameter using:
D² =(x₁ - x₂)² + (y₁ - y₂)²
This gives
D² = (1 + 3)² + (4 - 2)²
D² = 20
Take the square roots
D = 2√5
Divide by 2 to calculate the radius
r = √5
Square both sides
r² = 5
The equation of the circle is then represented as:
(x - a)² + (y - b)² = r²
This gives
(x + 1)² + (y - 3)² = 5
Hence, the equation of the circle is (x + 1)² + (y - 3)² = 5
Read more about circle equations at:
https://brainly.com/question/1559324
Related Questions
A baker has 15 cups of flour. He sets aside 4 cups of flour, and uses the rest for a cookie recipe that calls for 1/2 cup of flour. How many batches of cookies can the baker make? pls help ana2928
Answers
15-4= 11
11 x2=22
A triangle has side lengths of (6p – 7) centimeters, (7p – 2) centimeters,
and (6q – 9) centimeters. Which expression represents the perimeter, in
centimeters, of the triangle?
Answers
Given:
A triangle has side lengths of (6p – 7) centimeters, (7p – 2) centimeters,
and (6q – 9) centimeters.
To find:
The expression that represents the perimeter, in centimeters, of the triangle.
Solution:
We know that, perimeter of a triangle is the sum of its all sides.
[tex]Perimeter=(6p-7)+(7p-2)+(6q-9)[/tex]
Combining like terms, we get
[tex]Perimeter=(6p+7p)+6q+(-7-2-9)[/tex]
[tex]Perimeter=(13p)+6q+(-18)[/tex]
[tex]Perimeter=13p+6q-18[/tex]
Therefore, the perimeter of the triangle is represented by the expression [tex]13p+6q-18[/tex] centimeters.
A triangle has side lengths of (6p – 7) centimeters, (7p – 2) centimeters, and (6q – 9) centimeters.
To find:
The expression that represents the perimeter, in centimeters, of the triangle.
Answer:
-18+13p+6q
(Also got it right on a test)
Maria and her friends ate 5/8 of the 16 oranges that were at Maria's house. which is a reasonable answer for 5/8 x 16? please help!!
Answers
Answer:
10
Step-by-step explanation:
5(2). 8(2)
10/16
The answer is 10
how do you solve (7^-1)^-1 and 5^2 * 5^4 * 5^-3
Answers
Answer:
Step-by-step explanation:
exponents raised to a - power is an inverse function probably not the right word
a^-b = 1/(a^b) example 4^-2 = 1/(4^2) = 1/16
so (7^-1)^-1 is a double inverse which is back to the original number 7
inverted 7 twice
(7^-1)^-1 = (1/7)^-1 = 1/(1/7) = 7 trust me or use your calculator
since the coeffients are the same just add the powers... some exponent rule
5^2 * 5^4 * 5^-3 = 5^(2+4-3) = 5³
here is it written out
5^2 * 5^4 * 5^-3 = 5² × 5^4 × 5^-3 = (5×5) × (5×5×5×5) × (1/5×1/5×1/5)
5×5 × 5× (5×5×5 × 1/5×1/5×1/5) (5×5×5 × 1/5×1/5×1/5) = 1
5×5×5 = 5³
so
A local shelter is having an Adopt-a-thon for kittens and puppies. Kittens cost $50 to adopt and puppies are $75. The shelter made $1200 during the Adopt-a-thon event and adopted off twice as many puppies as kittens. Write and solve a system to find how many puppies and kittens were adopted
Answers
Answer:
Step-by-step explanation:
P=2K
50K+75P=1200, using P from above makes this equation become
50K+75(2K)=1200
50K+150K=1200
200K=1200
K=6, since P=2K
P=2(6)=12
So 12 puppies and 6 kittens were adopted.
Find the circumference of a circle with diameter 3 yd. use the value 3.14 for pie and do not round round the answer I’m looking for area and circumference
Answers
Circumference = pi * d = 9.42 yards
Is this a proportional graph?
Answers
Sorry its long but ill give brainlist to the right one just look at the images and multiple choice parts
Answers
If mAPW = 20°, then the measure of WPZ is
Answers
Answer:
The answer to the question is 20
because angle ZPA is 90°.
So,
It's 90-20 = 70°.
i can never understand these can someone help
Answers
Cross multiply.
15x=300
x=20
Therefore, the missing side is 20.
hi can someone please help
Answers
Answer:32
Step-by-step explanation:
B
A baby whale was born at the zoo. The baby
weighed 234.268 pounds. What is this number
rounded to the nearest hundredth?
a) 234.3
234:26
b) 234.26
c) 234.27
d) 234.268
Answers
Answer:
B I think hope it is right
Factor completely 64x2
Answers
Step-by-step explanation:
not factorable....rational numbers
Robert bought a pair of shoes that was on sale for 30% off
the original price of $79.95. Which is closest to the sale
price of the pair of shoes?
Answers
Answer:
The sale price of the shoes is $55.96
Step-by-step explanation:
1: 30% of $79.95 is 23.985.
Which would round to $23.99.
Then subtract 23.99 from 79.95.
79.95-23.99= 55.96
What is the área of this figure? (I need the answer bc this Is due in 1 hr )
Answers
Answer: 353ft
Step-by-step explanation:
To work out what the area of this composite shape is, you would split it into two shapes; a square and a rectangle.
For the formula of the rectangle and square you would do base x height.
So,
For the square you do 13x13=169
For the rectangle you would do 23x8=184
Then to work out the total area of the two shapes you would add the two areas together.
169+184=353
Select the correct answer.
If you roll a single six-sided die, what is the probability of rolling an odd number?
A 1/6
B 1/3
C 1/2
D 3
Please help!
Answers
Answer: that means you have a 3/6 chance which can be simplified to 1/2
1, 3 and 5 are the odd numbers
Step-by-step explanation:
Answer:
the answer is c 1/2
Step-by-step explanation:
since there are 6 numbers on the die that range from 1-6, that means there are three odd numbers, so the probability would be 3/6, which can reduce to 1/2
Evaluate the following expression if x=3: x^1
Answers
Answer:
3
Step-by-step explanation:
In ΔSTU, the measure of ∠U=90°, ST = 67 feet, and TU = 14 feet. Find the measure of ∠T to the nearest degree.
Answers
Answer:
78
Step-by-step explanation:
Answer:
78
Step-by-step explanation:
please help thank you
Answers
Answer:
n = 18
Step-by-step explanation:
(2n) and (n + 18) are vertically opposite angles and are congruent, then
2n = n + 18 ( subtract n from both sides )
n = 18
someone please do this for me... i will mark brainliest. all work needs to be shown. (picture shown above)
Answers
Step-by-step explanation:
just use step by step process so dum
The first equation is y = -2x + 8
and the second is
y = x - 4
Please show your work!!!
Answers
Answer:4
Step-by-step explanation:
y=-2x+8
y=x-4
Y equals the same thing so you can do equal values method
-2x+8=x-4
+2x +2x
__________
8=3x-4
+4 +4
_______
12=3x
_____
3 3
x=4
Explaination: Demos
Jason started last week with $900 in his checking account. During the week, he wrote the checks below. At the end of the week, jason recurved a paycheck for $534.59. He recorded all of these transactions in his check register. Evaluate jason’s check register. A. Jason did a good job; everything is correctly.
Answers
Answer:
D
Step-by-step explanation:
PLATO/ Edmentum
A recipe that makes 1 1/2 dozen cookies requires 3/4 cup of sugar. Shanika wants to make 6 dozen cookies. How many cups of sugar will she need
F. 1 1/8 cups
G. 4 cups
H. 6 3/4 cups
J. 3 cups
Answers
Answer:
h
Step-by-step explanation:
trust me js divide
Identify the slope of the graph below
Answers
Answer:
Positive
Step-by-step explanation:
Answer:
POSITIVE
Step-by-step explanation:
It's positive because the slope is rising like this /
If it was negative it would be declining like this \
hope that makes sense but I'm 1000% sure it's positive
What is an example of an irrational number besides pi?
Answers
0.3030030003...
An Irrational Number is a real number that cannot be written as a simple fraction. An irrational number cannot be written as a simple fraction.
7.1234 is irrational because it is a nonterminating, nonrepeating decimal.
65.4349224 is also irrational
---
hope it helps
If A > B, where on the number line will A appear?
Answers
Answer:
It will apear right after B and we can see it on the right side of B .
Max is asked to prove that LM=MN Here is hs proof.
This is not a correct proof explain why
Answers
Answer:
Its not true because:
Step-by-step explanation:
if you divide by M, with M not being 0, ypu have the equation L=N which is false
I need help
A line that includes the point (9, 10) has a slope of -1/9 what is its equation in point-slope
form?
Use the specified point in your equation. Write your answer using integers, proper fractions,
and improper fractions. Simplify all fractions.
Answers
Answer:
y -10 = -1/9 (x-9)
Step-by-step explanation:
Point slope form is
y-y1 = m (x-x1)
y -10 = -1/9 (x-9)
simplify to the lowest terms
Answers
Answer:
1/2
Step-by-step explanation:
divide the numerator & denominator by 4
Y= -6/5x-7 and y=2/5x+1
Answers
Answer:
x = -5
y = -1
Step-by-step explanation:
Y= -6/5x-7 and y=2/5x+1
then:
-6/5x - 7 = 2/5x + 1
simplify:
-8/5x = 8
divide both sides by 8:
-1/5x = 1
multiply both sides by 5:
-x = 5
x = -5
y = 2/5(-5) + 1 = -2 + 1 = -1