The equation of a circle with center (h,k) and radius r is given by (x−h)2+(y−k)2=r2 . For a circle centered at the origin, this becomes the more familiar equation
x2+y2=r2
.
How do you write the equation of a circle in center-radius form given its radius if the center is at the origin?
| Term Definition | Equation of a Circle If the center of a circle is (0, 0), then the equation of the circle is of the form x^2+y^2=r^2 , where r is the radius. | Radius The radius of a circle is the distance from the center of the circle to the edge of the circle. |
|---|
How do you write the equation of a circle given its radius and its center?
The center-radius form of the circle equation is in the format
(x – h)2 + (y – k)2 = r2
, with the center being at the point (h, k) and the radius being “r”. This form of the equation is helpful, since you can easily find the center and the radius.
What is the standard equation of a circle?
We know that the general equation for a circle is
( x – h )^2 + ( y – k )^2 = r^2
, where ( h, k ) is the center and r is the radius.
How do you write equation of a circle given its radius and its center at the origin What about if the center is at H k )?
The equation of a circle with center (h,k) and radius r is given by (x−h)2+(y−k)2=r2 . For a circle centered at the origin, this becomes the more familiar
equation x2+y2=r2
.
How do you write the standard form of a circle?
We know that the general equation for a circle is
( x – h )^2 + ( y – k )^2 = r^2
, where ( h, k ) is the center and r is the radius. So add 21 to both sides to get the constant term to the righthand side of the equation. Then complete the square for the y terms.
What is the equation of circle with Centre of origin and radius is 6 cm?
So, if the center is (0,0) and the radius is 6, an equation of the circle is:
(x-0)
2
+ (y-0)
2
= 6
2
.
What is the equation of the circle with center at the origin and a radius of 15 units?
We know that the general equation for a circle is
( x – h )^2 + ( y – k )^2 = r^2
, where ( h, k ) is the center and r is the radius. So add 21 to both sides to get the constant term to the righthand side of the equation. Then complete the square for the y terms.
What is the equation of a circle with a center at the origin and a radius of 12?
The equation of a circle, centered at the origin, is @$
begin{align*}x^2+y^2=r^2end{align*}@$
, where @$begin{align*}rend{align*}@$ is the radius and @$begin{align*}(x, y)end{align*}@$ is any point on the circle. Let's find the radius of @$begin{align*}x^2+y^2=16end{align*}@$ and graph.
What is a formula of cylinder?
The formula for the volume of a cylinder is
V=Bh or V=πr2h
. The radius of the cylinder is 8 cm and the height is 15 cm. … Therefore, the volume of the cylinder is about 3016 cubic centimeters.
How do you find the center of a circle given two points?
We know that the general equation for a circle is
( x – h )^2 + ( y – k )^2 = r^2
, where ( h, k ) is the center and r is the radius. So add 21 to both sides to get the constant term to the righthand side of the equation. Then complete the square for the y terms.
What is an example of standard form?
The standard form for linear equations in two variables is
Ax+By=C
. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.
How do you write the standard form of a circle with the center and point?
The standard form of a circle's equation is
(x-h)2 + (y-k)2 = r2 where (h,k)
is the center and r is the radius. To convert an equation to standard form, you can always complete the square separately in x and y.
How do you write the standard form of a circle with endpoints?
2 Answers By Expert Tutors. First, since you know the diameter endpoints, you can determine the center of the circle, which is the midpoint between those two points. So the equation of the circle will have the form
(x-3)
2
+(y-5)
2
=R
2
where R is the radius of the circle
.
What is the equation of the circle with center (- 4 7 and radius 6?
We know that the general equation for a circle is
( x – h )^2 + ( y – k )^2 = r^2
, where ( h, k ) is the center and r is the radius. So add 21 to both sides to get the constant term to the righthand side of the equation. Then complete the square for the y terms.
