Chapter 10.7 Notes: Write and Graph Equations of Circles

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Presentation transcript:

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 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

Ex. 1: Write the equation of the circle shown. Ex 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.

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.

Ex. 6: The point (3, 4) is on a circle whose center is (1, 4) 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.

Ex. 10: The equation of a circle is (x – 4)2 + (y + 3)2 = 16 Ex.10: The equation of a circle is (x – 4)2 + (y + 3)2 = 16. Graph the circle.

The epicenter is 4 miles away from B (4, 6). Ex.11: 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. 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).