Lesson 3 The Circle.docx - Lesson 3 The Circle Objectives At the end of the lesson you should be able to 1 Determine the equation of a circle in general

Lesson 3 The Circle.docx - Lesson 3 The Circle Objectives...

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Lesson 3. The Circle Objectives . At the end of the lesson, you should be able to: 1. Determine the equation of a circle in general and standard form 2. Reduce a given general equation of a circle to standard form 3. Graph a given equation of a circle 4. Solve problems on circle with some given conditions. Definition : A circle is a locus of a point that moves in a plane so that its distance from a fixed point remains constant. The fixed point is called the center , and the constant distance the radius of the circle. General Equation of a Circle The general equation of the second degree is of the form Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0. If A = C and B = 0, then the equation becomes Ax 2 + Ay 2 + Dx + Ey + F = 0 . This is the general equation of the circle for it can be shown that this equation can be reduced to the standard form by dividing through by A and then completing squares in x and y. If in the standard equation of a circle (x – h) 2 + (y – k) 2 = r 2 , r 2 = 0, the graph represents a point; r 2 > 0, the graph represents a circle; r 2 < 0, it has no graph.
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  • Summer '18
  • jane smeth

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