Find the equation of the circle with center coordinates of and a radius of. The equation of a circle is. The center is or, written another way. Substituting for and for , our formula becomes. Finally, the formula of the circle is. The standard form equation of a circle is , where is the center of the circle and is equal to the radius.
Thus, since we have the circle's standard form equation already given to us, we can ignore and , since all we need is. The area of circle is equal to , which is equal to. A circle has a center at 5,5 and a radius of 2. The circle has a center at 5,5 and a radius of 2. If the center of a circle is at 0,4 and the diameter of the circle is 6, what is the equation of that circle? Circle A is shifted up five units and left by six units.
Then, its radius is doubled. What is the new equation for circle A? We are then told that circle A is shifted up five units and then left by six units. This means that the y-coordinate of the center would increase by five, and the x-coordinate of the center would decrease by 6. Which of the following equations describes all the points x, y in a coordinate plane that are five units away from the point —3, 6? We are trying to find an equation for all of the points that are the same distance 5 units from —3, 6.
The locus of all points equidistant from a single point is a circle. In other words, we need to find an equation of a circle. The center of the circle will be —3, 6 , and the radius, which is the distance from —3,6 , will be 5. To begin, let us determine the point of intersection of these two lines by setting the equations equal to each other:. To find the y -coordinate, substitute into one of the equations.
Let's use y 1 :. Now, recall that the general form for a circle with center at x 0 , y 0 is:. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.
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Explanation : The equation of a circle is The center is or, written another way. Substituting for and for , our formula becomes Finally, the formula of the circle is.
On the xy plane, what is the area of a circle with the following equation:. Explanation : The standard form equation of a circle is , where is the center of the circle and is equal to the radius. Possible Answers: 3. Correct answer: 4. Explanation : The circle has a center at 5,5 and a radius of 2. Explanation : We are trying to find an equation for all of the points that are the same distance 5 units from —3, 6.
In this case, h will be —3, k will be 6, and r will be 5. Copyright Notice. Jonathan Certified Tutor. There are different forms to represent the equation of a circle,.
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. This general form is used to find the coordinates of the center of the circle and the radius, where g, f, c are constants. 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.
So, we will be using the completing the square formula to make a quick conversion from the general form to the standard form. 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. The distance between this point and the center is equal to the radius of the circle. Let's apply the distance formula between these points.
We take a general point on the boundary of the circle, say x, y. The polar form of the equation of the circle is almost similar to the parametric form of the equation of circle. We usually write the polar form of the equation of circle for the circle centered at the origin. The equation of a circle formula is used for calculating the equation of a circle. We can find the equation of any circle, given the coordinates of the center and the radius of the circle by applying the equation of circle formula.
So, let's apply the distance formula between these points. So, the equation of a circle is given by:. We will use the circle equation to determine the center and radius of the circle. The below-given image shows the graph obtained from this equation of the circle. There are so many different ways of representing the equation of circle depending on the position of the circle on the cartesian plane. We have studied the forms to represent the equation of circle for given coordinates of center of a circle.
There are certain special cases based on the position of the circle in the coordinate plane. Let's learn about the method to find the equation of circle for the general and these special cases. The simplest case is where the circle's center is at the origin 0, 0 , whose radius is r. Consider the case where the center of the circle is on the x-axis: a, 0 is the center of the circle with radius r.
Consider the case where the center of the circle is on the y-axis: 0, b is the center of the circle with radius r. Consider the case where the circumference of the circle is touching the x-axis at some point: a, r is the center of the circle with radius r.
If a circle touches the x-axis, then the y-coordinate of the center of the circle is equal to the radius r. Consider the case where the circumference of the circle is touching the y-axis at some point: r, b is the center of the circle with radius r.
If a circle touches the y-axis, then the x-coordinate of the center of the circle is equal to the radius r. Consider the case where the circumference of the circle is touching both the axes at some point: r, r is the center of the circle with radius r. If a circle touches both the x-axis and y-axis, then both the coordinates of the center of the circle become equal to the radius r, r. If a circle touches both the axes, then consider the center of the circle to be r,r , where r is the radius of the circle.
Here, r,r can be positive as well as negative. Here are the steps to be followed to convert the general form to the standard form:. We need to make sure that the coefficients of x 2 and y 2 are 1 before applying the formula.
The coordinates of the center of the circle can be found as: -g,-f. So, the center is 3,4. Let's see how to do this conversion. For this, expand the standard form of the equation of the circle as shown below, using the algebraic identities for squares:. Example 1: Find the equation of the circle in standard form for a circle with center 2,-3 and radius 3.
Example 2: Write the equation of circle in standard form for a circle with center -1, 2 and radius equal to 7. The equation of circle represents the locus of point whose distance from a fixed point is a constant value. This fixed point is called the center of the circle and the constant value is the radius of the circle. This general form is used to find the coordinates of the center of the circle and the radius of the circle. Here, c is a constant term, and the equation having c value represents a circle that is not passing through the origin.
To graph a circle equation, first find out the coordinates of the center of the circle and the radius of the circle with the help of the equation of the circle.
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