How to Find the Equation of a Circle With 3 Points
All ACT Math Resources
In the standard
Correct answer:
In the standard
Correct answer:
Explanation:
The general equation of a circle is
According to the question, 
The general equation for the area of a circle is
When we plug in 13 for 
A circle in the standard coordinate plane is tangent to the x-axis at (3,0) and tangent to the y-axis at (0,3). What is the equation of the circle?
Correct answer:
Explanation:
The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.
If a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point. If a circle is tangent to the y-axis at (0,3), this means it touches the y-axis at that point. Given these two points, we can determine the center and the radius of the circle. The center of the circle must be equidistant from any of the points on the circumference. This means that both (0,3) and (3,0) are the same distance from the center. If we draw these points on a coodinate plane, it becomes apparent that the center of the circle must be (3,3). This point is exactly three units from each of the given points, indicating that the radius of the circle is 3.
When we input this information into the formula for a circle, we get (x – 3)2+ (y – 3)2= 9.
Find the equation of the circle with center coordinates of 
Correct answer:
On the xy plane, what is the area of a circle with the following equation:
Correct answer:
A circle has a center at (5,5) and a radius of 2. If the format of the equation for the circle is (x-A)2+(y-B)2=C, what is C?
Explanation:
The circle has a center at (5,5) and a radius of 2. Therefore, the equation is (x-5)2+(y-5)2=22, or (x-5)2+(y-5)2=4.
If the center of a circle is at (0,4) and the diameter of the circle is 6, what is the equation of that 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 therefore radius = 3
(x-0) 2 + (y-4)2 = 32
x2 + (y-4)2 = 9
Circle A is given by the equation (x – 4)2 + (y + 3)2 = 29. Circle A is shifted up five units and left by six units. Then, its radius is doubled. What is the 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 general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.
Circle A first has the equation of (x – 4)2 + (y + 3)2 = 29. This means that its center must be located at (4, –3), and its radius is √29.
We are then told that circle A is shifted up five units and then left by six units. This means that the y-coordinate of the center would increase by five, and the x-coordinate of the center would decrease by 6. Thus, the new center would be located at (4 – 6, –3 + 5), or (–2, 2).
We are then told that the radius of circle A is doubled, which means its new radius is 2√29.
Now, that we have circle A's new center and radius, we can 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 answer is (x + 2)2 + (y – 2)2 = 116.
Which of the following equations describes all the points (x, y) in a coordinate plane that are five units away from the point (–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 are trying to find an equation for all of the points that are the same distance (5 units) from (–3, 6). The locus of all points equidistant from a single point is a circle. In other words, we need to find an equation of a circle. The center of the circle will be (–3, 6), and the radius, which is the distance from (–3,6), will be 5.
The standard form of a circle is given below:
(x – h)2 + (y – k)2 = r2, where the center is located at (h, k) and r is the length of the radius.
In this case, h will be –3, k will be 6, and r will be 5.
(x – (–3))2 + (y – 6)2 = 52
(x + 3)2 + (y – 6)2 = 25
The answer is (x + 3)2 + (y – 6)2 = 25.
What is the equation for a circle of radius 12, centered at the intersection of the two lines:
y 1 = 4x + 3
and
y 2 = 5x + 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, let us determine the point of intersection of these two lines by setting the equations equal to each other:
4x + 3 = 5x + 44; 3 = x + 44; –41 = x
To find the y-coordinate, substitute into one of the equations. Let's use y 1:
y = 4 * –41 + 3 = –164 + 3 = –161
The center of our circle is therefore: (–41, –161).
Now, recall that the general form for a circle with center at (x 0, y 0) is:
(x - x 0)2 + (y - y 0)2 = r 2
For our data, this means that our equation is:
(x + 41)2 + (y + 161)2 = 122 or (x + 41)2 + (y + 161)2 = 144
All ACT Math Resources
ACT Math Tutoring in Top Cities:
Atlanta ACT Math Tutoring, Austin ACT Math Tutoring, Boston ACT Math Tutoring, Chicago ACT Math Tutoring, Dallas Fort Worth ACT Math Tutoring, Denver ACT Math Tutoring, Houston ACT Math Tutoring, Kansas City ACT Math Tutoring, Los Angeles ACT Math Tutoring, Miami ACT Math Tutoring, New York City ACT Math Tutoring, Philadelphia ACT Math Tutoring, Phoenix ACT Math Tutoring, San Diego ACT Math Tutoring, San Francisco-Bay Area ACT Math Tutoring, Seattle ACT Math Tutoring, St. Louis ACT Math Tutoring, Tucson ACT Math Tutoring, Washington DC ACT Math Tutoring
ACT Math Tutors in Top Cities:
Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors
Report an issue with this question
If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.
DMCA Complaint
If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice ("Infringement Notice") containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.
Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.
Please be advised that you will be liable for damages (including costs and attorneys' fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.
Please follow these steps to file a notice:
You must include the following:
A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner's agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.
Send your complaint to our designated agent at:
Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105
Or fill out the form below:
How to Find the Equation of a Circle With 3 Points
Source: https://www.varsitytutors.com/act_math-help/how-to-find-the-equation-of-a-circle
0 Response to "How to Find the Equation of a Circle With 3 Points"
Post a Comment