Equation of a Circle in Standard and General Form

Introduction

The equation of the circle that we use provides us with an algebraic method to describe a circle. In simple terms, an equation represents the circle’s position on the cartesian plane. The equation is different from the formulas used to compute the circle’s circumference and area. It can be used across various problems related to circles in coordinate geometry. 

An equation is required to express a circle on a cartesian plane. If the length of the radius and the centre are known, we can draw a circle quickly on a paper piece. We will get to know all about this equation of a circle, its uses and Two Dimensions-Equation of a Circle in Standard and General Form from this article.

What is this equation of a circle?

It is an equation that represents and tells us the circle’s position on the cartesian plane. This equation gives us the algebraic method to describe a circle. The equation is different from the formulas used to compute the circle’s circumference and area.

The equation can be used across several problems related to circles in coordinate geometry. It is supposed to express a circle on a cartesian plane. A circle can be drawn easily on a paper piece if the length of the radius and the centre are known. The most important parts of the circle’s equation are Two Dimensions-Equation of a Circle in Standard and General Form.

Equations of circle types/forms

The circle’s equation is required to express a circle on a cartesian plane. If the centre and the length of the radius of a particular circle are known, we can easily draw it on a paper piece. If the centre’s coordinates and radius are known, we can draw a circle on a cartesian plane. There are several forms to express a circle. But this equation of circle has two dimensions: elevation of a Circle in Standard and General Form, which is the most important.

• Standard form
• Polar form
• General form
• Parametric form

General form: The equation used in this equation is x2 + y2 + 2gx + 2fy + c = 0. This is used to find the coordinates and the radius of the circle (g,f,c being constants). The general equation/form of the circle makes it a bit difficult to find meaningful properties about the given circle. Completing the square formula converts the general form to the standard form. This form is the most common one, and this circle’s equation has Two Dimensions-Equation of a Circle in Standard and in General Form that is used the most.

Standard form: This method gives the exact information regarding the centre and radius of the circle. It is effortless to read the centre and radius of the circle. The distance formula is applied between points. This is another part of this circle’s equation that is the most common, and it has Two Dimensions-Equation of a Circle in Standard and in General Form that we use commonly.

r=√((x2-x1)²+(y2-y1)²)

After this, when we square both sides, we get the standard form of the equation of the circle.

(x2-x1)²+(y2-y1)²=r2

Parametric form: The general form of this circle’s equation is the same as the parametric form of a circle’s equation. The point on the circle boundary is usually taken as (x,y). The joining of this point through a line and the centre of the circle (-h,-k) makes an angle θ. This equation is x2 + y2 + 2hx + 2ky + C = 0, in this x = -h + rcosθ and y = -k + rsinθ.

Polar form: This polar equation (a polar form of the equation) is comparable to the parametric form of this circle’s equation. The polar form of this circle’s equation is usually written for the circle centred at the origin.

We use a point P(rcosθ, rsinθ) on the circle’s boundary, r is the distance from the origin to the point. We have this equation of the circle centred at the origin, and we have the radius ‘p’, which is x2 + y2 = p2.

We substitute this value of x = rcosθ and y = rsinθ.

(rcosθ)2 + (rsinθ)2 = p2

r2cos2θ + r2sin2θ = p2

r2(cos2θ + sin2θ) = p2

r2(1) = p2

r = p

The formula for the equation of a circle

This circle’s equation is used to provide an algebraic method to describe a circle. The formulas used to calculate a circle’s area and circumference are different from this circle’s equation. This circle’s equation is used in various problems across circles in coordinate geometry.

This circle’s equation represents a circle’s position in a cartesian plane. We can note this circle’s equation if we have the length and coordinates of the circle’s centre. A circle represents a locus of points with a constant value of the distance from a fixed point. We use two-equations of a circle the most times, Two Dimensions-Circle’s equation in Standard and General Form; these are the two most common forms.

Conclusion

This equation of the circle that we use provides us with an algebraic method to describe a circle. This circle’s equation is very different from the formula that we use to compute the circumference and the area of a circle. This circle’s equation is used widely in many problems of circles in coordinate geometry.

This circle’s equation is required to express a circle on the cartesian plane. If the length of its radius and the centre of the circle are known, we can draw a circle. We can also draw a cartesian plane if we have the coordinates of the radius and the centre of the circle.