10 1 Equations of a Circle Standard Equation

10. 1 Equations of a Circle Standard Equation of a Circle Definition of a Circle

Definition of a Circle A circle is a set of points a given distance from one point called the center. The distance from the center is called the radius

Standard equation of the circle If the circle is at the origin x 2+y 2=r 2 r is the radius If the circle is not at the origin The center is at (h, k)

Standard equation of the circle If the circle is at the origin x 2+y 2=r 2 r is the radius If the circle is not at the origin Solve for r

Write the equation of Circle Center at ( -5, 0) and radius 4. 8 h =? k =? r = 4. 8

Write the equation of Circle Center at ( -5, 0) and radius 4. 8 h =-5 k =0 r = 4. 8

Write the equation of Circle Center at ( 4, -3) and a point on the circle (2, 1) h= k= r= x= y=

Write the equation of Circle Center at ( 4, -3) and a point on the circle (2, 1) h=4 k=-3 r= x=2 y=1

Write the equation of Circle Center at ( 4, -3) and a point on the circle (2, 1) h=4 k=-3 r 2 = 20 x=2 y=1

Given the equation of the Circle (x – 13)2 + (y – 6)2 = 52 Tell if the point is inside or outside the circle. (5, 6)

Given the equation of the Circle (x – 13)2 + (y – 6)2 = 52 Tell if the point is inside or outside the circle. (5, 6) (5 -13)2 + (6 – 6)2 is it <, >, or = 52 ( - 8)2 + 02 = 64 = 25 Greater then outside the circle. Less then Inside the circle. Equal is on the circle.

Given the equation of the Circle (x – 13)2 + (y – 6)2 = 52 Tell if the point is inside or outside the circle. (5, 6) Outside (14, 8)

Given the equation of the Circle (x – 13)2 + (y – 6)2 = 52 Tell if the point is inside or outside the circle. (5, 6) Outside (14, 8) In (20, 9)

Given the equation of the Circle (x – 13)2 + (y – 6)2 = 52 Tell if the point is inside or outside the circle. (5, 6) Outside (14, 8) In (20, 9) Outside

Given the equation of the Circle (x – 13)2 + (y – 6)2 = 52 Tell if the point is inside or outside the circle. (5, 6) Outside (14, 8) In (20, 9) Outside (16, 2)

Given the equation of the Circle (x – 13)2 + (y – 6)2 = 52 Tell if the point is inside or outside the circle. (5, 6) Outside (14, 8) In (20, 9) Outside (16, 2) On

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