SAT Math assist » Geometry » name: coordinates Geometry » circles » just how to discover the equation of a circle

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

Explanation:

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

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

Explanation:

The formula for the equation that a circle is:

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

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

You are watching: A circle has its center at (−1, 2) and a radius of 3 units. what is the equation of the circle?

h = 0 and also k = 4

and diameter = 6 because of this radius = 3

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

x2 + (y-4)2 = 9

Circle A is offered by the equation (x – 4)2 + (y + 3)2 = 29. One A is change up five units and also left by six units. Then, the radius is doubled. What is the brand-new equation for circle A?

Explanation:

The general equation that a one is (x – h)2 + (y – k)2 = r2, where (h, k) represents the place of the circle\"s center, and r represents the size of that radius.

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

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

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

Now, the we have circle A\"s brand-new center and radius, we have the right 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 price is (x + 2)2 + (y – 2)2 = 116.

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### Example inquiry #1 : just how To discover The Equation of A circle

Which the the following equations explains all the point out (x, y) in a coordinate aircraft that are 5 units far from the allude (–3, 6)?

(x – 3)2 – (y + 6)2 = 25

(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

Explanation:

We space trying to discover an equation for all of the point out that room the exact same distance (5 units) from (–3, 6). The locus of every points equidistant native a solitary point is a circle. In various other words, we require to uncover an equation that a circle. The facility of the circle will be (–3, 6), and the radius, i beg your pardon is the distance from (–3,6), will certainly be 5.

The standard type of a one is given below:

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

In this case, h will certainly be –3, k will be 6, and also r will certainly 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 concern #1 : how To discover The Equation that A one

What is the equation for a circle of radius 12, focused at the intersection of the two lines:

y1 = 4x + 3

and

y2 = 5x + 44?

(x + 41)2 + (y + 161)2 = 144

(x - 22)2 + (y - 3)2 = 12

(x - 41)2 + (y - 161)2 = 144

None of the various other answers

(x - 3)2 + (y - 44)2 = 144

(x + 41)2 + (y + 161)2 = 144

Explanation:

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

4x + 3 = 5x + 44; 3 = x + 44; –41 = x

To uncover the y-coordinate, substitute into one that the equations. Let\"s use y1:

y = 4 * –41 + 3 = –164 + 3 = –161

The center of ours circle is therefore: (–41, –161).

Now, recall the the general kind for a one with facility at (x0, y0) is:

(x - x0)2 + (y - y0)2 = r2

For our data, this means that our equation is:

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

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### Example question #1 : exactly how To find The Equation of A circle

The diameter the a circle has actually endpoints in ~ points (2, 10) and also (–8, –14). Which of the complying with points does not lie top top the circle?

(–8, 10)

(–8,–12)

(9,3)

(–15, –7)

(2, –14)

(–8,–12)

Explanation:  Report an Error

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

A circle exists completely in the an initial quadrant such the it intersects the -axis in ~ . If the circle intersects the -axis in at least one point, what is the area that the circle?    Explanation:

We are given two really important pieces of information. The very first is the the one exists completely in the an initial quadrant, the 2nd is that it intersects both the - and -axis.

The truth that it is totally in the an initial quadrant way that it can not go past the two axes. Because that a circle to crossing the -axis in much more than one point, it would necessarily relocate into another quadrant. Therefore, we have the right to conclude it intersects in specifically one point.

The intersection that the circle with must also be tangential, since it have the right to only crossing in one point. We can thus conclude the the circle must have both - and - intercepts equal to 6 and have a center of .

This leaves us through a radius of 6 and also an area of: Report an Error

### Example concern #1 : just how To uncover The Equation the A one

We have actually a square with size 2 sitting in the an initial quadrant through one corner touching the origin. If the square is inscribed within a circle, find the equation of the circle. Explanation:

If the square is inscribed within the circle, in means the facility of the circle is at (1,1). We require to also find the radius the the circle, which wake up to be the size from the corner of the square come it\"s center. Now usage the equation of the circle v the center and also .

We get Report an Error

### Example question #1 : one

What is the radius the a circle with the equation ? Explanation:

We require to broaden this equation to and then finish the square.

This brings us to .

We leveling this come .

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

A circle has actually its origin at . The point is ~ above the sheet of the circle. What is the radius that the circle?

There is not sufficient information to answer this question. Explanation:

The radius of the one is equal to the hypotenuse that a ideal triangle v sides the lengths 5 and 7.   This radical can not be reduced further.

See more: M A Downward Shift In The Consumption Function Can Be Caused By:

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