Determine the equation of the circle whose circumference is 14*pi and the center is (3,-2).
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,544 answers
starTop subjects are Math, Science, and Business
We have to find the equation of the circle whose circumference is 14pi and the center is (3,-2).
Now the circumference of a circle is given by 2*pi*r where r is the radius. Here 2*pi*r = 14*pi
=> r = 14*pi / 2*pi
=> r = 7
Now the equation of a circle with center (h,k) and radius r is (x-h)^2 +(y-k)^2 = r^2
Using the values we have here in the equation we get:
(x- 3)^2 + (y+2)^2 = 49
Therefore the equation of the circle is (x- 3)^2 + (y+2)^2 = 49.
Related Questions
- Circle equation.Determine the equation of the circle whose circumference is 14*pi and the center...
- 1 Educator Answer
- Calculate the circumference and area of the circle whose diameter = 14.
- 2 Educator Answers
- A circle has the equation x^2+y^2+2x-2y-14=0, determine the center and radius.
- 1 Educator Answer
- What is the circumference of the circle whose area is 25pi ?
- 2 Educator Answers
- What is the circumference of the circle whose area is 24 cm^2.
- 2 Educator Answers
calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Given the circumference of a circle is 14pi and the center is at the point (3,-2).
We need to determine the equation of the circle.
First, we need to write into the standard form of the circle:
(x-a)^2 + ( y-b)^2 =r^2 where (a,b) is the center and r is the radius.
==> (x-3)^2 + ( y+2)^2 = r^2.
Now we need to find the radius of the circle.
Given the circumference C = 14pi.
==> 2*r*pi = 14pi
==? r= 14pi/ 2pi = 7
Then the radius of the circle is 7.
==> (x-3)^2 + ( y+2) = 7^2
==> (x-3)^2 + ( y+2)^2 = 49
The equation of the circle in the standard form is:
(x-h)^2 + (y-k)^2 = r^2
if the circumference of the circle is 14pi, we can compute the radius of the circle:
2*pi*r = 14pi
We'll divide by 2pi:
r = 14pi/2pi
r = 7
We'll identify the coordinates of the circle:
h = 3 and k = -2
The equation of the circle is:
(x-3)^2 + (y+2)^2 = 49
Student Answers