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Locate Earthquake's Epicenter with Circles

Learn how to find an earthquake's epicenter using seismograph data and graphing circles. Understand why three seismographs are necessary for accurate pinpointing.

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Locate Earthquake's Epicenter with Circles

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  1. EXAMPLE 4 Graph a circle The equation of a circle is (x – 4)2 + (y + 2)2= 36. Graph the circle SOLUTION Rewrite the equation to find the center and radius. (x – 4)2 + (y +2)2 = 36 (x – 4)2 + [y – (–2)]2 = 62 The center is (4, –2) and the radius is 6. Use a compass to graph the circle.

  2. The epicenter of an earthquake is the point on Earth’s surface directly above the earthquake’s 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 earthquake’s epicenter. EXAMPLE 5 Use graphs of circles EARTHQUAKES Use the seismograph readings from locations A, B, and Cto find the epicenter of an earthquake.

  3. EXAMPLE 5 Use graphs of circles • 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). SOLUTION The set of all points equidistant from a given point is a circle, so the epicenter is located on each of the following circles.

  4. ANSWER The epicenter is at about (5, 2). EXAMPLE 5 Use graphs of circles • Awith center(–2, 2.5)and radius7 • Bwith center(4, 6)and radius4 • Cwith center(3, –2.5)and radius5 To find the epicenter, graph the circles on a graph where units are measured in miles. Find the point of intersection of all three circles.

  5. for Examples 4, and 5. GUIDED PRACTICE 5. The equation of a circle is (x – 4)2 + (y + 3)2 = 16. Graph the circle. SOLUTION

  6. for Examples 4, and 5. GUIDED PRACTICE 6. The equation of a circle is (x + 8)2 + (y + 5)2 = 121. Graph the circle. SOLUTION

  7. for Examples 4, and 5. GUIDED PRACTICE 7. Why are three seismographs needed to locate an earthquake’s epicenter? SOLUTION Two circles intersect in two points. You would not know which one is the epicenter, so you need the third circle to know which one it is.

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