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• #Circle equation calculator how to

The following are some solved problems for finding the equation of a circle in both cases, such as when the circle’s center is an origin and when the center is not an origin.Įxample 1: Consider a circle whose center is at the origin and whose radius is 8.

#Circle equation calculator how to

The following formulas are given for circles in terms of radius.Īrea= π(radius)2 How to Find the Equation of the Circle? Therefore, it is a circle having a real center and imaginary radius. G² + f² c, then the radius of the circle is real. X² + y² + 2gx + 2fy + c = 0, represents the circle with centre (−g,−f) and radius equal to a² = g² + f²− c. Since, (x+g)² = x²+ 2gx + g² and (y+f)² =y² + 2fy + f² substituting the values in equation (1), we haveĬomparing (2) with (x−h)² + (y−k)² = a², where (h, k) is the center and ‘a’ is the radius of the circle. X² + y² + 2gx + 2fy + c = 0, for all values of g, f and c.Īdding g2 + f2 on both sides of the equation gives, The general equation of any type of circle is represented by: Which is called the standard form for the equation of a circle.

In this case, the equation of the circle with center (h, k)and radius ‘a’ is, X²+y² = (radius)² Equation of a Circle When the Centre is not an OriginĬ(h, k) represents the center of the circle, and P(x, y) represents any point on the circle. We can apply Pythagoras’ theorem to the problem as follows: The base of the triangle is the distance along the x-axis, while the height is the distance along the y-axis. The radius of the circle is the hypotenuse of the right triangle formed by the perpendicular line drawn from point (x) to the x-axis. Imagine that (x,y) is a point on a circle, and that the center of the circle is (0,0). We know that the distance between the point (x, y) and the origin (0,0)can be calculated using the distance formula, which is equal toĪ circle whose center serves as its origin has the equation: Let ‘a’ be the radius of the circle that is equal to OP. Imagine an arbitrary point P(x, y) on the circle. Equation of a Circle When the Centre is Origin Circle equations are presented here in all their forms, such as standard and general forms, with examples. Since a function is defined by its values associated with one point in the codomain, while the line that passes through the circle intersects it at two points.Ĭircles are described mathematically by equations. Circles are not functions, as it should be clear. The question of whether a circle can be considered a function arises in the case of circles. X²+y²−2x−4y-11 = 0 Equation Of Circle Is Function or Not? Therefore, the equation of this circle will be: If we know the coordinates of the circle’s center and its radius, we can easily find its equation.Īs an example: Let’s say point (1,2) is the center of the circle, and the radius is equal to 4 cm. A circle with a center of (h,k) and a radius of r has the following equation: The circumference is defined as the distance between all points on a curve from the fixed point, called the center, and all points on that curve. As we shall see in this article, the standard form of an equation of a circle and examples of an equation of a circle whose center occurs at the origin and one whose center does not occur at the origin are discussed. Circle radius refers to the distance between a point on the circumference and the center. Known as the center of the circle, this fixed point is the fixed point of the circle. R is the radius of the circle, and (h,k) is the coordinates of the circle’s center.īefore we deduce the equation for a circle, let us discuss what is a circle? A circle is a set of all points that are equally spaced from a fixed point in a plane.

How to Use the Equation of a Circle Calculator?