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A circle with center (xo, yo) and radius r has an equation of the form:
(x - xo)2 + (y - yo)2 = r2
which can be rearranged to:
x2 - 2xox + xo2 + y2 - 2yoy + yo2 = r2
⇒ x2 - 2xox +y2 - 2yoy + xo2 + yo2 - r2 = 0
or x2 - 2xox +y2 - 2yoy = r2 - xo2 - yo2
So depending how your equation is given, the center can be read directly from the equation (first form above) or is -1/2 times the coefficients of the x and y terms. eg:
What is the center of the circle with equation x2 - 4x + y2 + 6y + 12 = 0
The coefficients of the x and y terms are -4 and +6, so the center is -1/2 times these, namely; (2, -3).
Fully rearranging the circle's equation:
x2 - 4x + y2 + 6y + 12 = 0
⇒ (x - 2)2 - 4 + (y + 3)2 - 9 + 12 = 0 [completing the squares]
⇒ (x - 2)2 + (y + 3)2 - 1 = 0
⇒ (x - 2)2 + (y + 3)2 = 1
⇒ circle has centre (2, -3) and radius 1.
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The center of a circle is located at c(3-13). The x-axis is tangent to the circle at (30). Find the equation of the circle?
Equation of the circle: (x-3)^2 +( y+13)^2 = 169
How do you find the general form equation of a circle?
There are probably several ways to approach it; one general equation for the circle is: (x - a)2 + (y - b)2 = r2 This describes a circle with center at coordinates (a, b), and with a radius of r.
How do you find the center or midpoint of a circle given one endpoint of the diameter?
to be honest I dont know
Find the center and radius of the circle with this equation x2 plus y2 plus x equals 0?
x2+y2+4x+2y+3=0(x+2)2 + (Y+2.5)2 = 3This is the equation of circle with center at (-2,-2.5) with radius 3.5
Find an equation of the circle that has center 0 2 and passes through the origin.?
The equation of a circle with center (0,2) and radius r is x^2+(y-2)^2=r^2 Since it passes through (0,0) (the origin) 0^2+(0-2)^2=r^2 r^2=4 The equation of the circle is x^2+(y-2)^2=4
What is a chord passing through the center of a circle?
a diameter
Find the center of a circle with the equation x2 plus y2-18x-14y plus 124?
The center of the circle is at (9, 7) on the Cartesian plane
The center of a circle is located at c(3-13). The x-axis is tangent to the circle at (30). Find the equation of the circle?
Equation of the circle: (x-3)^2 +( y+13)^2 = 169
Where is the center of the circle given by the equation x - 3 2 plus y plus 2 2 equals 9?
(3, -2) You find the center by taking the opposite of the numbers added to the X and to the Y.
How do you find the area of a circle if the diameter is given?
multiple the diameter by 2 to get the radius, then use your equation and go from there
How do you find the general form equation of a circle?
There are probably several ways to approach it; one general equation for the circle is: (x - a)2 + (y - b)2 = r2 This describes a circle with center at coordinates (a, b), and with a radius of r.
How do you find the center or midpoint of a circle given one endpoint of the diameter?
to be honest I dont know
Find the center and radius of the circle with this equation x2 plus y2 plus x equals 0?
x2+y2+4x+2y+3=0(x+2)2 + (Y+2.5)2 = 3This is the equation of circle with center at (-2,-2.5) with radius 3.5
Find an equation of the circle that has center 0 2 and passes through the origin.?
The equation of a circle with center (0,2) and radius r is x^2+(y-2)^2=r^2 Since it passes through (0,0) (the origin) 0^2+(0-2)^2=r^2 r^2=4 The equation of the circle is x^2+(y-2)^2=4
How do you find circumference given radius?
2 pi rthis is the equation of the circumference of a circle. just multiply out 2 times pi(3.14159) times the radius that you were given.
How do you figure square feet using a circumference?
Square feet are a measure of area, and the area of a circle is usually given by the equation: a = πr2 The circumference of a circle is given with the equation: c = 2πr To find the area of the circle given only it's circumference, we can rearrange the circumference equation, solving it for r, and then substituting it into our radius equation in place of r. c = 2πr r = c / 2π a = πr2 a = π(c / 2π)2 a = πc2 / 4π2 a = c2/π So the area of a circle is equal to the square of it's circumference divided by pi.
How do you find radius of circle if you know the area?
The area of a circle is given by the equation A=πr2.To solve for r, divide both sides by π, then take the square root of both sides of the equation.This leaves you with the equation r=sqrt(A/π)
