Equations of Circles - Middletown High School



Estimate the values of any radicals in your given point to the nearest tenth, then plot your point on the coordinate grid below.What kind of figure has been formed?Find the distance between your point and the origin (0, 0).Just as an equation of a line represents the relationship between the x & y coordinates of the points that make up the line, an equation of a circle can also represent the relationship between the x & y coordinates of the points that make up the circle.What do ALL of the points on the circle have in common?Would every point (x, y) on the circle have this same property?OK, let’s fill in a distance of 8 between the points (x, y) and (0, 0) using the distance formula:d= (x2-x1)2+(y2-y1)2This equation is pretty messy, can we clean it up a bit?ToolKit: Equations of CirclesA circle is a collection of points that are all __________ __________ from a single point (called the __________).The distance from any point on a circle to the center is called the __________.An equation that represents all points on a circle centered at the origin can be written using the formula:Ex. A circle with radius 5 is centered at the origin.Equation:Graph:Equations of CirclesWrite an equation for each circle:Center ( 0, 0 ), radius = 4Center ( 0, 0 ), radius = 9Center ( 0, 0 ), radius = 7Center ( 0, 0 ), diameter = 12Center ( 0, 0 ), diameter = 4Center ( 0, 0 ), diameter = 23Endpoints of diameter are ( -7, 0 ) and ( 7, 0 )Endpoints of diameter are ( 0, 3 ) and ( 0, -3 )Determine if the given point is on the circle:Point: ( -5, 12 )Circle: x2+y2= 169Point: ( 8, -6 )Circle: x2+y2= 100Point: ( ? , ? )Circle: x2+y2= 1Point: ( -1,3)Circle: x2+y2= 4Write an equation for the circle shown in each graph: _________________________ _________________________Sketch a graph of the circle with each given equation:x2+y2= 36x2+y2= 25x2+y2= 64x2+y2= 49x2+y2= 9x2+y2= 100 ................
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