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**Graphing and Writing Equations**

Circles Graphing and Writing Equations

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**What is a circle? A conic formed when…. A second degree equation…**

A locus of points…

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Definition as a conic A circle is a conic or a conic section because it is formed by the intersection of a plane and a double-napped cone.

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**Algebraic Definition A circle is defined as the second degree equation**

Ax2+Bxy+Cy2 +Dx+Ey+F = 0 when A = C.

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**A circle is a locus of points…..**

But, what is a locus…? A locus is the set of all points, and only those points, that satisfy one or more conditions. So, “ A locus of points in a plane 10 cm from a point A” gives a geometric description of a circle with center A and a radius of 10

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Geometric Definition A circle is the locus or collection of all points (x, y) that are equidistant from a fixed point, (h, k) called the center of the circle. The distance r , between the center and any point on the circle is the radius

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**Using the distance formula, you can derive**

the standard form of a circle. (x- h)2 + (y- k)2 = r 2 where, center = (h, k) and radius = r

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Equation of a circle: Practice Problems to write the equation of a circle when given the center and the radius.

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**What if the center and radius are not given?**

Try these : Center = (0,3) and solution point = (0, 6) Endpoints of diameter are (-2,3) and (6,5) Center on the line y = 2, and tangent to the x-axis at (3,0)

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Graph the circle To graph a circle, locate all the points that are a fixed distance r, from the center (h, k). Click here to graph a circle

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**Graph a circle with center at the origin**

Example: Graph x2 + y2 = 4

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**To Graph a Circle center (h,k) and radius r**

Example: (x-3)2+ (y-3)2 =4 Click Here To graph a circle if given a radius and a center

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**What are some applications?**

Circular orbits of the earth for satellites. Perfect shape for cross-section of a submarine. Gears Other

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