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The Circle I. Homework II. Conic Sections We will see that the conic sections can be formed by intersecting a plane with a cone. A demo will be done in class. III. Circles A circle is the set of points in a plane a fixed distance from a point. By the Pythagorean Theorem, we have that the distance r from the center (h,k) of the circle to a point (x,y) on the circle is r = sqrt[(x - h)2 + (y - k)2] or (x - h)2 + (y - k)2 = r2 Example: Find the equation of the circle with center (2,1) and radius 4. Solution: We have: (x - 2)2 + (y - 1)2 = 42 = 16 Exercise: A) Find the equation of the circle with center (1,3) and passing through the point (7,11) Graph the following: A) (x - 2)2 + (y + 1)2 = 9 B) x2 - 2x + y2 + 6y = 14 C) x2 + y2 + 4x - 4y = 9 D) x2 + y2 + 6x + 2y = 29 E) Find the area between the circles: x2 + y2 - 6x + 4y = 12 and x2 + y2 - 6x + 4y = 23
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