caption: Intersection Form of the Circle Equation
exif: {"Image DocumentName": "Intersection Form of the Circle Equation", "Image ImageDescription": "9/14/2018. Intersection Form of the Circle Equation. 1. Radius r. Centre C(a,b) We have derived the general equation of any circle with centre (a,b) and radius \u00ae, this is given at the top of the slide. We can re-write this equation into a different format given at the bottom of the slide. The reason for doing so, is that this format can be much more useful when dealing with certain types of questions. To get to this equivalent form we multiply out the bracket in our original equation. Then we gather each of the different terms together. Then we equate the LHS of the equation to zero, by subtracting r squared from each side. We then we tidy up the equation further by letting g= - a , f = -b and the constant term c = a squared plus b squared minus r squared. This gives us the equivalent form of the general equation at the bottom of the slide. Note that in this format the centre is given by (-g, -f ) since a=-g and b=-f. Also by rearranging the expression for c we can deduce the formula for the radius r. r=square root of g2+f2-c. Radius r. Centre C(-g,-f) Sep", "Image XResolution": "200", "Image YResolution": "200", "Image ResolutionUnit": "Pixels/Inch", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}