In this article, we will discuss the equation of the circle also the standard equation of a circle in an easy way. The equation of a circle comes in two forms. If the equation of a circle is in standard form, we can easily identify the center of the circle (h,k) and radius r

**The set of all points in the plane that are equally distance from a fixed point is called a circle.** The fixed point is called the **center **of the circle and the distance from the center of the circle to any point on the circle is called the **radius of the circle**.

If C(h,k) is centre of a circle, r its radius and P(x, y) any point on the circle, then the circle,

denoted S(C ; r) in set notation is

By the distance formula, we get

\;\;\left|\overline{CP}\right|=\sqrt{(x-h)^2+(y-k)^2}=ror \;\;(x-h)^2+(y-k)^2=r^2\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(1)

is an equation of circle in standard form.

If the center of the circle is the origin, then (1) reduces to

\left|\overline{CP}\right|=\sqrt{x^2+y^2}=r^2If r = 0, the circle is called a point circle which consists of the Centre only.

Let P(x, y) be any point on the circle (2) and let the inclination of OP be q as shown in the figure. It is clear that

\begin{array}{r}x=r\;\cos\theta\;\;,\;\;\;y=r\;\sin\theta\end{array}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(3)

The point P(r\cos\theta,r\sin\theta) lies on (2) for all values of \theta. Equations (3) are called **parametric equations **of the

circle (2).

Now it’s time to discuss the examples of “What is the Equation of a Circle” or write the standard equation of a circle.

**Example 1:** Write an equation of the circle with centre (-3, 5) and radius 7.**Solution:** The required equation is

Here (h,k)=(-3, 5) and r=7 ,So

\left|\overline{CP}\right|=\sqrt{(x+3)^2+(y-5)^2}=7^2.

x^2+y^2+6x-15y-10=0Which is the required equation of circle.

you can also see the topic conic section.