Example Write down the equation of a circle alongwith radius 8 & center ( -4, 7 ) .
Solution
Okay, in this case we have r =8 , h = -4 and k = 7 thus all we have to do is plug them into the standard form of the equation of circle.
( x - ( -4))^{2 }+ ( y - 7 )^{2} = 82
(x+ 4)^{2} + ( y - 7 )^{2} = 64
Do not perform square of the two terms on the left. Leaving these terms as they will allow us to rapidly identify the equation as that of a circle and to rapidly identify the radius and center of the circle.
Graphing circles is a properly simple procedure once we know the radius & center. In order to graph a circle all we actually need is the right most, left most, top most & bottom most points on the circle. Once we know these it's simple to sketch in the circle.
Nicely adequate for us these points are simple to find. As these are points on the circle we know that they have to be a distance of r from the center. Thus the points will have the following coordinates.
right most point : ( h + r, k )
left most point : ( h - r, k )
top most point : ( h, k +r )
bottom most point : (h, k - r )
In other terms all we have to do is add r on to the x coordinate or y coordinate of the point to obtain the right most or top most point respectively and subtract r from the x coordinate or y coordinate to obtain the left most or bottom most points.