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10.6 Equations of Circles Advanced Geometry
What do you need to find the equation of a circle? Coordinates of the Center of the circle. Radius – Distance from center to a point on the circle
Let’s Look at a Circle
Break it Down Given: Center is (h,k), the radius is r, and (x,y) is a point on the circle. The distance between (x,y) and (h,k) is r… so let’s use the distance formula.
Break it Down
Standard Equation of a Circle (x – h)² + (y – k)² = r² Where the center is at (h,k) & The radius is r
Example Write the standard equation of a circle that has a center at the origin and a radius of 5.
Example Write the standard equation of a circle with center (-5, 0) and radius 4.8.
Example The point (2,1) is on a circle whose center is (4,-3). Write the standard equation of the circle.
Example The point (0, -1) is on a circle whose center is (-4, 1). Write the standard equation of the circle.
Graphing The equation of a circle is (x + 2)² + (y – 3)² = 9. First find the center and the radius of the circle, and then graph the circle.
Graphing Graph (x – 3)² + (y + 1)² = 4
Applying Graphs of Circles The equation of a circle is (x – 13)² + (y – 6)² = 9. Three points are located as follows: A(5, 6), B(14, 8), and C(20, 9). Which point is in the circle?
Graphs and Equations of Circles Book: Math 3 (Green Book) Section: 5.2.
Objectives Write equations and graph circles in the coordinate plane.
Notes Over 10.3 r is the radius radius is 4 units
Advanced Algebra Trigonometry Appendix B
CIRCLES Unit 3-2. Equations we’ll need: Distance formula Midpoint formula.
The Distance Formula & Equations of Circles
[x – (–8)] 2 + (y – 0) 2 = ( 5 ) 2 Substitute (–8, 0) for (h, k) and 5 for r. Write the standard equation of a circle with center (–8, 0) and radius 5.
10.7 Write and Graph Equations of Circles Hubarth Geometry.
GeometryGeometry Lesson 75 Writing the Equation of Circles.
Equations of Circles 10.6 California State Standards 17: Prove theorems using coordinate geometry.
Standard Form for the Equation of the Circle
9-8 Equations of Circles Objectives: To write and use the equation of a circle in the coordinate plane.
Graphs and Equations of Circles (might want some graph paper) Book: Math 3 (Green Book) Section: 5.2 Circles Quiz: Thursday Circles Test: Sept. 17.
GEOMETRY HELP [x – (–8)] 2 + (y – 0) 2 = ( 5 ) 2 Substitute (–8, 0) for (h, k) and 5 for r. Write the standard equation of a circle with center (–8, 0)
1.3 Symmetry; Graphing Key Equations; Circles
Square both sides to find the standard equation of a circle with radius r and center (h, k). Finding Equations of Circles You can write an equation of.
Unit 1 – Conic Sections Section 1.2 – The Circle Calculator Required.
Making graphs and solving equations of circles.
Circles in the Coordinate Plane I can identify and understand equations for circles.
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