Writing the Equation of a Circle - Softschools.com.
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Find the Equation of a Circle Given Its Center and One Point on Its Circumference. Find the equation of a circle with center point coordinate of (3,4) and a point P (-1,3) Click input boxes to enter data. Center point coordinates (3,4) ( h, k ) Any Point coordinates, for example (-1,3) on its circumference ( x, y ).
Use the formula, where (h,k) is the center and (x,y) is an arbitrary point on the circle. In this case, and. Also, and. Plug these values into the equation above and simplify to get: So because, , and, this means that the equation of the circle that passes through the points (-6,1) and (4,-5) (which are the endpoints of the diameter) is.
Equation of a Circle A circle is the set of all points in a plane at a given distance (called the radius ) from a given point (called the center.) A line segment connecting two points on the circle and going through the center is called a diameter of the circle.
If the circle center is at the origin. The equation is then a little simpler. Since the center is at the origin, h and k are both zero. So the general form becomes which simplifies down to the basic form of the circle equation: For more on this see Basic Equation of a Circle. Parametric form.
Given the circumference of a circle is 14pi and the center is at the point (3,-2). We need to determine the equation of the circle. First, we need to write into the standard form of the circle.
Exercise worksheet on 'How to convert an equation of a circle from general form to standard form.' This page includes a lesson covering 'how to convert an equation of a circle from general form to standard form' as well as a 15-question worksheet, which is printable, editable, and sendable. Converting an equation of a circle from general form to standard form.