![]() ![]() We know that the general form of the equation of a circle is x 2 y 2 2hx 2ky C = 0. Squaring both sides, we get the standard form of the equation of the circle as:Ĭonsider this example of an equation of circle (x - 4) 2 (y - 2) 2 = 36 is a circle centered at (4,2) with a radius of 6. Let's apply the distance formula between these points. The distance between this point and the center is equal to the radius of the circle. The standard equation of a circle with center at \((x_1, y_1)\) and radius r is \( (x - x_1)^2 (y - y_1)^2 = r^2\), where (x, y) is an arbitrary point on the circumference of the circle. The standard equation of a circle gives precise information about the center of the circle and its radius and therefore, it is much easier to read the center and the radius of the circle at a glance. So, we will be using the completing the square formula to make a quick conversion from the general form to the standard form. Unlike the standard form which is easier to understand, the general form of the equation of a circle makes it difficult to find any meaningful properties about any given circle. This general form is used to find the coordinates of the center of the circle and the radius, where g, f, c are constants. The general form of the equation of a circle is: x 2 y 2 2gx 2fy c = 0. Let's look at the two common forms of the equation of circle-general form and standard form of the equation of circle here along with the polar and parametric forms in detail. There are different forms to represent the equation of a circle, Using the equation of circle, once we find the coordinates of the center of the circle and its radius, we will be able to draw the circle on the cartesian plane. A circle can be drawn on a piece of paper given its center and the length of its radius. 1.Īn equation of circle represents the position of a circle on a cartesian plane. In this article, let's learn about the equation of the circle, its various forms with graphs and solved examples. A circle can be represented in many forms: Similarly, on a Cartesian plane, we can draw a circle if we know the coordinates of the center and its radius. A circle can be drawn on a piece of paper if we know its center and the length of its radius. To represent a circle on the Cartesian plane, we require the equation of the circle. This equation is used across many problems of circles in coordinate geometry. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle. You do the same thing (multiply, divide add or subtract) to bothīy doing the same thing to both sides of the equation you can find what one x is equal to.The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation will remain balanced only if Way to solve equations by thinking of the two sides of the equationĪs two sides of a balance. This button restarts the difficulty level but will present different equations. A Restart button is provided if the questions generated start to become a little too difficult. It is not possible to predict how quickly you will develop confidence solving equations of a particular type but typically the examples will increase in difficulty very slightly each time you press the Next button. You canĬhange the options so that one of five different types of equation Make up unlimited equations for you to practise solving. To find which value is represented by the letter x. There will be no powers (squared, cubed etc). In simple terms it is a mathematical sentence in which youĬan see only one letter (which might appear more than once) but A linear equation is an equation in which each term is either aĬonstant or the product of a constant times the first power of a ![]()
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