In the standard

name: coordinates plane, what is the radius and also the facility of the circle ?Explanation:

When finding the center and radius of circle

, the facility is and the radius is . Notice that they space not an adverse even though in the equation lock have an unfavorable signs in front. This becomes vital when taking care of real numbers. Also, notification the square of .You are watching: What is the equation of a circle whose center is at the origin and whose radius is 9?

Our circle,

has the same principles applied as the above principle, therefore is ours center. Notification how the numbers signs have been switched. This is the instance for all circles because of the an adverse in the basic equation above.To uncover the radius of a circle, you should take the number the equation is same to and square source it. This is because of the square of

stated above. The . Use the least common multiples the 27 to discover that three 3’s comprise 27. Take two threes out together the square source of a number multiply by itself is itself. This leaves one 3 under the radical. As such our radius is .Center:

Radius:Report an Error

### Example question #2 : just how To find The Equation the A one

In the standard

coordinate plane, what is the area that the circle ?**Possible Answers:**

**Correct answer:**

Explanation:

The general equation of a circle is

.According come the question,

. Thus, .The general equation because that the area of a circle is

.When we plugin 13 for

, we gain our area to same .Report an Error

### Example inquiry #1 : exactly how To discover The Equation of A one

A circle in the typical coordinate aircraft is tangent come the x-axis in ~ (3,0) and tangent to the y-axis at (0,3). What is the equation that the circle?

**Possible Answers:**

**Correct answer:**

Explanation:

The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the works with of the center of the circle, and also r to represent the radius of the circle.

If a circle is tangent come the x-axis in ~ (3,0), this method it touch the x-axis at the point. If a circle is tangent come the y-axis at (0,3), this means it touches the y-axis at that point. Offered these 2 points, we can determine the center and also the radius of the circle. The facility of the circle have to be equidistant from any of the point out on the circumference. This method that both (0,3) and also (3,0) room the very same distance indigenous the center. If we draw these points on a coodinate plane, that becomes obvious that the center of the circle need to be (3,3). This allude is exactly three units from each of the offered points, indicating the the radius that the circle is 3.

When us input this info into the formula because that a circle, we acquire (x – 3)2 + (y – 3)2 = 9.

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### Example inquiry #4 : exactly how To uncover The Equation that A one

Find the equation that the one with facility coordinates the

and a radius of .**Possible Answers:**

**Correct answer:**

Explanation:

The equation of a one is

The center is

or, written another method . Substituting for and for , ours formula becomesFinally, the formula the the one is

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### Example concern #5 : just how To discover The Equation that A circle

On the xy plane, what is the area of a circle through the adhering to equation:

**Possible Answers:**

**Correct answer:**

Explanation:

The standard kind equation of a one is

, whereby is the facility of the circle and is same to the radius. Thus, because we have the circle"s standard type equation currently given to us, we can ignore and , due to the fact that all we need is .The area of circle is same to

, i m sorry is equal to .Report an Error

### Example question #1 : just how To find The Equation that A circle

A circle has a facility at (5,5) and also a radius of 2. If the format of the equation for the circle is (x-A)2+(y-B)2=C, what is C?

**Possible Answers:**

3

4

1

5

2

**Correct answer:**

4

Explanation:

The circle has actually a facility at (5,5) and a radius the 2. Therefore, the equation is (x-5)2+(y-5)2=22, or (x-5)2+(y-5)2=4.

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### Example inquiry #1 : just how To uncover The Equation that A one

If the facility of a one is at (0,4) and also the diameter that the circle is 6, what is the equation of the circle?

**Possible Answers:**

x2 + y2 = 9

(x-4)2 + y2 = 9

x2 + (y-4)2 = 36

x2 + (y-4)2 = 9

(x-4)2 + y2 = 36

**Correct answer:**

x2 + (y-4)2 = 9

Explanation:

The formula for the equation of a circle is:

(x-h) 2 + (y-k)2 = r2

Where (h,k) is the center of the circle.

h = 0 and k = 4

and diameter = 6 thus radius = 3

(x-0) 2 + (y-4)2 = 32

x2 + (y-4)2 = 9

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### Example question #8 : how To discover The Equation that A circle

Circle A is provided by the equation (x – 4)2 + (y + 3)2 = 29. Circle A is shifted up 5 units and left by six units. Then, its radius is doubled. What is the brand-new equation for circle A?

**Possible Answers:**

(x – 2)2 + (y + 2)2 = 58

(x – 10)2 + (y + 8)2 = 116

(x + 2)2 + (y – 2)2 = 58

(x – 10)2 + (y + 8)2 = 58

(x + 2)2 + (y – 2)2 = 116

**Correct answer:**

(x + 2)2 + (y – 2)2 = 116

Explanation:

The basic equation that a circle is (x – h)2 + (y – k)2 = r2, where (h, k) to represent the place of the circle"s center, and r to represent the length of that radius.

Circle A first has the equation of (x – 4)2 + (y + 3)2 = 29. This means that its facility must be situated at (4, –3), and also its radius is √29.

We room then told that circle A is shifted up 5 units and then left by 6 units. This method that the y-coordinate the the center would rise by five, and the x-coordinate that the facility would diminish by 6. Thus, the new center would be situated at (4 – 6, –3 + 5), or (–2, 2).

We room then told the the radius of circle A is doubled, which means its new radius is 2√29.

Now, that we have actually circle A"s new center and radius, we deserve to write its general equation using (x – h)2 + (y – k)2 = r2.

(x – (–2))2 + (y – 2)2 = (2√29)2 = 22(√29)2 = 4(29) = 116.

(x + 2)2 + (y – 2)2 = 116.

The prize is (x + 2)2 + (y – 2)2 = 116.

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### Example concern #9 : how To find The Equation that A one

Which of the complying with equations describes all the point out (x, y) in a coordinate plane that are five units far from the suggest (–3, 6)?

**Possible Answers:**

(x – 3)2 + (y + 6)2 = 5

(x + 3)2 + (y – 6)2 = 25

y + 6 = 5 – (x – 3)2

(x – 3)2 + (y + 6)2 = 25

(x – 3)2 – (y + 6)2 = 25

**Correct answer:**

(x + 3)2 + (y – 6)2 = 25

Explanation:

We room trying to find an equation for every one of the point out that are the same distance (5 units) indigenous (–3, 6). The locus of every points equidistant native a single point is a circle. In various other words, we need to uncover an equation of a circle. The facility of the circle will certainly be (–3, 6), and the radius, which is the distance from (–3,6), will be 5.

The standard kind of a one is offered below:

(x – h)2 + (y – k)2 = r2, where the facility is located at (h, k) and also r is the length of the radius.

In this case, h will certainly be –3, k will be 6, and also r will be 5.

(x – (–3))2 + (y – 6)2 = 52

(x + 3)2 + (y – 6)2 = 25

The price is (x + 3)2 + (y – 6)2 = 25.

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### Example question #1 : just how To find The Equation the A circle

What is the equation for a one of radius 12, centered at the intersection the the two lines:

*y*1 = 4*x* + 3

and

*y*2 = 5*x* + 44?

**Possible Answers:**

(x - 3)2 + (y - 44)2 = 144

(x - 22)2 + (y - 3)2 = 12

None of the other answers

(x + 41)2 + (y + 161)2 = 144

(x - 41)2 + (y - 161)2 = 144

**Correct answer:**

(x + 41)2 + (y + 161)2 = 144

Explanation:

To begin, allow us determine the point of intersection of these 2 lines by setup the equations equal to every other:

4*x* + 3 = 5*x* + 44; 3 = *x* + 44; –41 = *x*

To uncover the *y*-coordinate, substitute right into one the the equations. Let"s usage *y*1:

*y* = 4 * –41 + 3 = –164 + 3 = –161

The facility of our circle is therefore: (–41, –161).

See more: 3 Million Pennies Worth In Dollars, Is A Million Pennies? 3 Million Pennies In Dollars

Now, recall that the general form for a circle with facility at (*x*0, *y*0) is:

(*x* - *x*0)2 + (*y* - *y*0)2 = *r*2

For ours data, this method that ours equation is:

(*x* + 41)2 + (*y* + 161)2 = 122 or (*x* + 41)2 + (*y* + 161)2 = 144

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