Sec 1.8 Circles

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Sec 1.8 Circles

• Objectives
• To understand the distance and midpoint formulas.
• To understand the equations of circles and their
  graphs.

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Distance Formula

The distance between the points A(x1, y1) and
B(x2, y2) in the plane is
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Ex 1. Find the distance between (-2,8) and (4,-4)
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Midpoint Formula
The midpoint of the line segment from A(x1, y1)
to B(x2, y2) is
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Ex 2. Find the midpoint between (-2,8) and
(4,-4)
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Class Work

• Which of the points P(1, 2) or Q(8, 9) is
  closer to the point A(5, 3)?
• Show that the quadrilateral with vertices
  P(1, 2), Q(4, 4), R(5, 9), and S(2, 7) is a
  parallelogram by proving that its two diagonals
  bisect each other.

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Definition of a Circle

• A circle is the set of all points P(x, y) whose
  distance from the center C(h, k) is r.

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Equation of a Circle

• The equation of a circle with center (h,k) and
  radius r is given by

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Ex 3. Find the equation of a circle with center
(2, -5) and radius 3.
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Ex 4. Show that the equation represents a
circle, and find the center and radius of the
circle.

• x2 6x y2 2y 43

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Class Work

• 3. Find the equation of a circle that has
  endpoints of a diameter that are P(-1, 1) and
  Q(5, 9).
• 4. Show that x2 y2 2x 6y 7 0 is a
  circle and find the center and radius.

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Class Work

• 5. Show that x2 y2 6y 2 0 is a circle
  and find the center and radius.
• 6. Show that 3x2 3y2 6x 12y 0 is a
  circle and find the center and radius.

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HW p97 1-13 odd, 27,29, 81-93 odd