Warm upO Find the coordinates of the midpoint of
the segment that has endpoints at (- 5, 4) and (7, -2).
O Find the distance between points at (10, 7) and (- 4, 8)
Lesson 10-2 Circles
Objective: To use and determine the standard and general forms of the
equation of a circleTo graph circles
Degenerate ConicsO formed when the plane passes thru
the vertex of the double right cone.
degenerate
ellipse
degenerate
hyperbola
degenerate
parabola
CircleO a set of points in a plane which are
equidistant from a given point. (the center)
O Radius – the distance from the center to any point on the circle.
CircleOThe Standard Form of a circle with a center at
(0,0) and a radius, r, is……..
OFrom Pythagorean Theorem
222 ryx
center (0,0)radius = 2
Copyright ©1999-2004 Oswego City School District Regents Exam Prep Center
Circles
Now if the center moves off of the origin to point (h, k) we can use the distance formula to find the radius.
(x, y)
(h, k)
22 )()( kyhxr
222 )()( kyhxr
CirclesOThe Standard Form of a circle with a center at
(h,k) and a radius, r, is……..
222 )()( rkyhx
center (3,3)radius = 2
Copyright ©1999-2004 Oswego City School District Regents Exam Prep Center
Example 1OWrite the standard form of the
equation of the circle that is tangent to the x-axis and has its center at (-5, 4). Then graph the equation.
Example 2OThe equation of a circle is:
Write the standard form of the equation. divide by 4
complete the
square
51162444 22 yxyx
4
51___)4(___)6( 22
yyxx4
514622
yxyx
494
51)44()96( 22
yyxx
4
1)2()3( 22 yx
Example 3O Write the standard form of the equation of
the circle that passes through the points at (1,1), (1, 2), and (2, 3). Then identify the center and radius of the circle.
O Use the general equationO Use each point as x and y to create 3 new
equations and solve the system for D, E and F.
O Once found substitute D, E and F back into the original equation and complete the square (twice) to create the equation of the circle.
022 FEyDxyx
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