The exploration is carried out by changing the parameters h, k and r included in the standard equation \( (x - h)^2 (y - k)^2 = r^2\). Interactive Tutorials to Explore the Equation of a Circle More tutorial on equation of circle are included in this site. \( (x^2 3)^2 - 3^2 (y^2 - 1)^2 - (-1)^2 5 = 0 \)Ĭompare the above equation to the standard one \( (x - h)^2 (y - k)^2 = r^2\) and identify the coordinates \( h \) and \( k \) of the center of the circle and the radius \( r \). Put, between parentheses, terms in \( x\) and \( x^2 \) together and the terms in \( y \) and \( y^2\) togetherĬomplete the square of each binomial within the parehtheses Rewrite the equation of the circle given by \( x^2 y^2 6x - 2y 5 = 0 \) and find its center and radius. The circle found above and the three points are shown in the graph below.Įxample 5 Rewrite the general equation of a circle into standard form. We now substitute \( A \), \( B \) and \( C \) by their values and write the equation of the circle as follows: The square root in the above equation may be eliminated by squaring both sides of the equation to obtain Working with square root add extra difficulties that can be avoided. To find the equation, we use the definition to write that distance \( CM \) is equal to the radius \( r \) The distance from the center \( C(,h,k) \) to a point \( M(x,y) \) on the circle is given by This distance between \( C \) and any point on the circle is called the radius and has length \( r \) in the graph below. In other words, a circle of center \( C \) is the set of all points that are at equal distance from point \( C \). By definition, all points \( M(x,y) \) on the circle are at equal distance from the center. Equation of a Circle Equation of a Circle in Standard FormĪ circle with center \( C \) given by its coordintaes \( C (h,k) \) is shown below.
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