At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Answer:
Step-by-step explanation:
x²-8x+16+y²+2y+1=16+1-13
(x-4)²+(y+1)²=2²
general form of a circle's equation is
(x-h)^2 + (y-k)^2 = r^2
Where (h,k) is the center and r= radius
By comparing with A,
(4,-1) is center and radius= 2.
The center of the circle is (-4,2) and the radius is 2
How to determine the center and the radius?
The equation is given as:
x^2 + y^2 - 8x + 2y + 13 = 0
Rewrite as:
x^2 - 8x + y^2 + 2y + 13 = 0
Subtract 12 from both sides
x^2 - 8x + y^2 + 2y = -13
Group each variable
[x^2 - 8x] + [y^2 + 2y] = -13
-------------------------------------------------------------------
Take the coefficient of x and y
-8 and 2
Divide by 2
-4 and 1
Square both numbers
16 and 1
-------------------------------------------------------------------
Next, we add 16 and 1 to both sides of the equation
[x^2 - 8x + 16] + [y^2 + 2y + 1] = -13 + 16 + 1
Express as perfect squares and evaluate the sum
(x - 4)^2 + (y + 1)^2 = 4
Express 4 as 2^2
(x - 4)^2 + (y + 1)^2 = 2^2
A circle is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where:
Center = (a,b)
Radius = r
This means that the center of the circle is (-4,2) and the radius is 2
Read more about circle equation at:
https://brainly.com/question/1559324
#SPJ9
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
