write the standard form of the equation of the circle for which the endpoints of a diameter are (0,0) and (4,-6)

Answers

Answer 1

Given:

The endpoints of a diameter are (0,0) and (4,-6).

To find:

The equation of the circle.

Solution:

The endpoints of a diameter are (0,0) and (4,-6). So, the length of the diameter is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d=\sqrt{(-6-0)^2+(4-0)^2}[/tex]

[tex]d=\sqrt{36+16}[/tex]

[tex]d=\sqrt{52}[/tex]

[tex]d=2\sqrt{13}[/tex]

Now, radius is half of the diameter.

[tex]r=\dfrac{2\sqrt{13}}{2}[/tex]

[tex]r=\sqrt{13}[/tex]

Center of the circle is the midpoint of the endpoints of a diameter.

[tex]Center=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]Center=\left(\dfrac{0+4}{2},\dfrac{0+(-6)}{2}\right)[/tex]

[tex]Center=\left(\dfrac{4}{2},\dfrac{-6}{2}\right)[/tex]

[tex]Center=\left(2,-3\right)[/tex]

Standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where, (h,k) is center and r is radius.

The center of the circle is (2,-3) and radius is [tex]\sqrt{13}[/tex]. So,

[tex](x-2)^2+(y-(-3))^2=(\sqrt{13})^2[/tex]

[tex](x-2)^2+(y+3)^2=13[/tex]

Therefore, the standard form of the circle is [tex](x-2)^2+(y+3)^2=13[/tex].


Related Questions

PLEASE HELP!!!! ❗❗❗❗❗❗❗
I NEED THE ANSWER TO THIS ASAP!!! PLS HELP!!! question below ;-;

the track team is trying to reduce their time for a relay race. First they reduced their time by 2.1 minutes. Then they are able to reduce that time by 1/10. If their final time is 3.96 minutes, what was their beginning time? Show or explain your reasoning.

Answers

Answer:

6.27 minutes

Step-by-step explanation:

3.96+2.1=6.06

1/10=0.1x2.1=0.21+6.06=6.27

The Econ motel charges $260 for 4 nights, how much would they charge for 7 nights?

Answers

Answer:

$455

Step-by-step explanation:

To find the answer, divide 260 by 4 to find the cost of one night. This gets us 65. Now, we multiply 65 by 7 to get 455. This means it costs $455 for 7 nights.

Answer:

$455

Step-by-step explanation:

260 divided by 4 is 64

64 times 7 is 455

You are purchasing a car for $12,465.00 plus 5.65% sales tax. You make a $1,300.00 down payment and have a fair credit score. If you improved your credit score to good and paid $1,500 on your purchase, how much interest could you save in the first month?

Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75. 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40



$13.25


$14.68


$21.74


$25.69

Answers

Answer:

21.74

Step-by-step explanation:

Kelsea and Landon are playing in a park standing 100 feet away from each other. They both see a bird flying above them. The angles of elevation from each person to the bird are shown. How high is the bird from the ground? Round your answer to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

use an ASA triangle  with law of sine

since we know that 180 = 20 +45 + C   .. solve for C = 115°

now use  law of sines    c/ sin(C) = b/sin(B) .. and solve for b

Sin(20)*100/sin(115) = b

b = 37.73774 ft

that's the hypotenuse of the 45 triangle

SOH CAH TOA   to remember how trig functions fit

use b*Cos(45) = adj

26.6846 = adj

The bird is 26.7 ft. from the ground

PLEASE ANSWER ASSAP!!!!!!!!!!!!!!!! WILL GIVE BRAINLEST!!!!!!!!!!!!!!!!!!!

Answers

Answer:B

Step-by-step explanation:

Vertical angles are equal, so 4x - 20 = 60

If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).
I can’t find it

Answers

Answer:

[tex](f-g)(x)=2x-3[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]f(x)=3x-1\text{ and } g(x)=x+2[/tex]

And we want to find:

[tex](f-g)(x)[/tex]

This is equivalent to:

[tex]=f(x)-g(x)[/tex]

By substitution:

[tex]=(3x-1)-(x+2)[/tex]

Simplify. Distribute:

[tex]=(3x-1)+(-x-2)[/tex]

Rearrange:

[tex]=(3x-x)+(-1-2)[/tex]

Therefore:

[tex](f-g)(x)=2x-3[/tex]

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!

Answers

Answer:

4.5 would be the answer

Step-by-step explanation:

Help me i don't understand this and i need a answer fast <3

Answers

Answer:

what grade r u in?

Step-by-step explanation:

Solve the inequality

Answers

Answer:

x ≥ -64

Step-by-step explanation:

"3/4ths of a number is greater than or equal to -48"

3/4 of a number ≥ -48

Let's say the number is x.

(3/4)x ≥ -48

Multiply both sides by 4.

3x ≥ -192

Divide both sides by 3.

x ≥ -64

can u pls help me with this question ​

Answers

Answer:

c

Step-by-step explanation:

divide 1/5,280 and then multiply that by 6,600

Answer:

the answer is c

Step-by-step explanation:

multiply 6,600 by 1 and that will give you 6,600 again

after that you divide 6,600 and 5,280 that will get you 1.25

if you think I'm wrong just do it on the calculator it will give you 1.25

have a nice day!!

Circle geometry please help,

Answers

Answer:

7. Inscribed angle

Step-by-step explanation:

7. Inscribed angle

8.

y° = 70°

z° = 140°

8. y° and 70° are the measures of the angles subtended in the same arc. So, they would be equal.

Therefore, y° = 70°

Measure of central angle is two times the measure of the inscribed angle.

Therefore,

z° = 2* 70° = 140°

Draw 9:10 on a clock

Answers

Answer:

put the short hand at nine

Step-by-step explanation:

put the long hand and 10 minutes

Answer:

you can draw on your notebook and draw the clock

HELPPP PLASE ITS DUE REALLY SOOOONNNNNNNNNNNN!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

4 sorry of its not right

The math clubs car can travel 9 meters in a second. The race track for the soap box derby is 63 meters long. How many seconds will it take the Math clubs car to make it around the track

Answers

Answer: it will take 7 seconds

Step-by-step explanation: 9 x 7 = 63

Pete walks 2 miles in an hour. At this rate how many miles can Pete walk in 4 hours

Answers

Answer:

8 miles

Step-by-step explanation:

2 miles= an hour

4 miles= two hours

6 miles= three hours

8 miles = four hours

Answer:

8

Step-by-step explanation:

Use Pete's walking speed: 2 miles per hour × 4 hours = 8 miles.

Simplify:
3 [23 + (4 – 2)3 – (6 - 2)2]
A. 3

B. 12
D. 24

E-3

Answers

Answer:63

Step-by-step explanation:

Find the point that maximizes the objective functions P=2x+5y using constraints:
y>=10-2x
y<=7-1/2x
x>=0
y>=0​

Answers

Answer:

(2,6)

Step-by-step explanation:

28
6. Hannah has 229 horse stickers and
164 kitten stickers. How many more
horse stickers than kitten stickers does
Hannah have?

Answers

Subtract 229 and 164 its 65 so thats your answer .

what number is 0.001 more than 437.999

Answers

Answer:

437.999 + 0.001 = 438

Step-by-step explanation:

What is the area of a circle if it has a diameter of 14 units

Answers

Answer:

143.94 is the area of the circle

3/2+b=7/4 what is the value of B

Answers

b = 1/4

b = 0.25

Move all terms not containing  b  to the right side of the equation.

Answer:

b=1/4

Step-by-step explanation:

Beth is making fruit salad. She adds 4 grapes for every 2 strawberries. If she uses 20 strawberries, how many grapes will she use?

Answers

Answer:40

Step-by-step explanation:2x+4x where the 4 represents every clump of 4 grapes and the 2 is strawberries

PLEASE HELP ASAP!!!!

Answers

A and B are polynomial. E,D,C are not because polynomial can’t have a negative exponents, or a division by a variable.

pls help !! - Using the graph below, what is the rule for a translation form point A to point D?

Answers

The answer is b trust me I got this one right

Answer:

B

Step-by-step explanation: i took the test on docs/forms

3x + y = 15 and y = 2x
The solution, given in (x,y) form is

Answers

Answer: (3, 6)

Step-by-step explanation:

3x + y = 15

y = 2x

Using substitution:

3x + 2x = 15

5x = 15

x = 15/5

x = 3

y = 2x

y = 2 * 3

y = 6

x = 3

y = 6

= (3, 6)

the price of a sweater was reduced from 20$ to 12$ by what percentage was the price of the sweater reduced

Answers

Answer:

11%

Step-by-step explanation:

the answer is 11 because you need to minus

11% okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

What is the slope of a perpendicular line through -y=-2x+8?

A) -1/2
B) -2
C) 2
D) 1/2

Answers

I think it is b hope it’s write

Answer:

c. 2

Step-by-step explanation:

-y=-2x+8

I hope this helps

14. Quadrilateral ABCD is located at A(2,0), B(3,-4), and C(7,-5). What are the
coordinate of point D that makes the quadrilateral a rhombus?
PLEASE HELPPP

Answers

Answer:

A

Step-by-step explanation:

A rhombus is a quadrilateral whose four sides all have the same length. if you look at the picture I sent, A(6,-1) forms a rhombus where all of the sides are an equal length.

Can some one help me please

Answers

Answer:

B

Step-by-step explanation:

x+2+10 is 13 which is the beginning of the perimeter

I think it’s B I’m not for sure

A giant tortoise moves at a slow but steady pace. It takes
the giant tortoise 3 seconds to travel 10.5 inches.
How many inches will the tortoise travel in 1 second?

Answers

the answer should be that it will take the tortoise 1 second to travel 3.5 inches
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