Chapter 10.7 Notes: Write and Graph Equations of Circles - PowerPoint PPT Presentation

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Chapter 10.7 Notes: Write and Graph Equations of Circles

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Chapter 10.7 Notes: Write and Graph Equations of Circles Goal: You will write equations of circles in the coordinate plane. Equations of Circles You can write the ... – PowerPoint PPT presentation

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Title: Chapter 10.7 Notes: Write and Graph Equations of Circles


1
Chapter 10.7 Notes Write and Graph Equations of
Circles
  • Goal You will write equations of circles in the
    coordinate plane.

2
  • Equations of Circles
  • You can write the equation of any circle if you
    know its radius and the coordinates of its
    center.
  • Standard Equation of a Circle
  • The standard equation of a circle with center
    (h, k) and radius, r is
  • (x h)2 (y k)2 r2

3
  • Ex.1 Write the equation of the circle shown.
  • Ex.2 Write the standard equation of a circle
    with center (0, -9) and radius 4.2.

4
  • Write the standard equation of the circle with
    the given center and radius.
  • Ex.3 Center (0, 0), radius 2.5
  • Ex.4 Center (-2, 5), radius 7
  • Ex.5 The point (-5, 6) is on a circle with
    center (-1, 3). Write the standard equation of
    the circle.

5
  • Ex.6 The point (3, 4) is on a circle whose
    center is
  • (1, 4). Write the standard equation of the
    circle.
  • Ex.7 The equation of a circle is
  • (x 4)2 (y 2)2 36. Graph the circle.
  • Ex.8 The equation of a circle is
  • (x 8)2 (y 5)2 121. Graph the circle.
  • Ex.9 The point (-1, 2) is on a circle whose
    center is (2, 6). Write the standard equation of
    the circle.

6
  • Ex.10 The equation of a circle is
  • (x 4)2 (y 3)2 16. Graph the circle.

7
  • Ex.11 The epicenter of an earthquake is the
    point on Earths surface directly above the
    earthquakes origin. A seismograph can be used to
    determine the distance to the epicenter of an
    earthquake. Seismographs are needed in three
    different places to locate an earthquakes
    epicenter.
  • Use the seismograph readings from locations A,
    B, and C to find the epicenter of an earthquake.
  • The epicenter is 7 miles away from A (-2, 2.5).
  • The epicenter is 4 miles away from B (4, 6).
  • The epicenter is 5 miles away from C (3, -2.5).
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