What is the general form of the equation for the given circle?

A circle is one of those geometrical figures that can be represented using different equations. Its standard equation can be written in different formats including the standard equation of a circle. Mostly, problems involve the conversion to the general form of the equation of a circle using the given parameters.

It is done to make the equation simple and learn about the circle in detail. There are multiple benefits of converting an equation of a circle to its general form. This guide will show you how to write an equation of a circle in its general form.

How to find the general form of the equation of a circle?

Learning the method of writing the general equation of a circle involves understanding the formula. If you don’t know the simplest formula/equation of a circle, you can’t understand the way to write its general form.

Here is the simplest equation representing a circle.

x2 + y2 = r2

Here, “x” and “y” represents the vertices of the center of the circle while “r” represents the radius of the circle. Normally, the question states “Write the general equation of the circle using specific coordinates of the center”. In this regard, the above equation will become:

(x - x0)2 + (y - y0)2 = r2

TIn this equation, “x0 and “y0 are the new coordinates of the center of the circle. Using this formula, you can write the general form of the equation of a circle. To make the process easier and get assistance in completing your work, you can use our Equation of a Circle calculator.

This online calculator will perform the calculation and show you different equations for a circle using your given values. It will take a few seconds to display the answer on your computer/mobile screen. Just copy the answer and put it in your assignment for the final answer.

How to calculate the general equation of a circle?

Calculator’s Bag has the core aim to educate its readers properly and let them understand the concerned math questions. So, we have solved an example here for your understanding.

example1:

Write the general equation of a circle having center (3, 7) and radius 4.

Solution:

We only have to put the values in the following formula,

(x - x0)2 + (y - y0)2 = r2

By putting the values,

(x - 3)2 + (y - 7)2 = (4)2

x2 + 9 -6x + y2 + 49 - 14y = 16

The solution of the above equation is,

x2 + y2 -6x - 14y + 43= 0

This is the general equation of the circle.

Conclusion

This guide has comprehensively discussed the way of finding the equation of a circle step by step with a solved example. If you are facing problems while solving the equations, you can get assistance from our Equation of a Circle Calculator. It will enable you to get the equation of any circle within seconds of the input values.

FAQ

How do you write the equation of a circle in general form?

We can write the equation of a circle in general form using the following formula:

(x - x0)2 + (y - y0)2 = r2

What is the general form of a circle example?

The general of the circle is given by,

x2 + y2 = r2

Is the standard form and general form the same?

No, the standard form and general form of the equation of a circle are not the same.

How do you find the equation of a circle that passes through the origin?

To find the equation of a circle that passed through the origin, the values for “x0” and “y0 will be “0” and the equation will become the general equation of the circle.

What is the general form of a circle example?

The general form of a circle having a radius “3” will be written as:

x2 + y2 = 9

How do you convert a general equation of a circle to standard form?

We can convert the general equation of a circle into the standard form by completing the square of the related terms given in the general equation.