Mastery Check

Show What You Know

The Lopez and Bell families are next door neighbors and both have dogs. They have electric fences that need to be recalibrated so they are one foot behind the property line ( y-axis). The center of each circle is the location of the electric fence beacon and cannot be changed.

Write the equations of the circles to represent the current range of the electric fences for both families.

$Lopez family (- 12.5, 1.5), C (- 5.5, 1.5) r = \sqrt{{(- 12.5 - (- 5.5))}^{2} + {(1.5 - 1.5)}^{2}} r = 7 {(x - (- 5.5))}^{2} + {(y - 1.5)}^{2} = 7^{2} {(x + 5.5)}^{2} + {(y - 1.5)}^{2} = 49$

$Bell family (- 1, 4), C (5, 4) r = \sqrt{{(- 1 - 5)}^{2} + {(4 - 4)}^{2}} r = 6 {(x - 5)}^{2} + {(y - 4)}^{2} = 6^{2} {(x - 5)}^{2} + {(y - 4)}^{2} = 36$

Write and graph the new equation for the Bell family that will stay within the property.

$(1, 4), C (5, 4) r = \sqrt{{(1 - 5)}^{2} + {(4 - 4)}^{2}} r = 4 {(x - 5)}^{2} + {(y - 4)}^{2} = 4^{2} {(x - 5)}^{2} + {(y - 4)}^{2} = 16$

The Lopez family has the new equation in general form. Write the equation in standard form and graph. $x^{2} + y^{2} + 11 x - 3 y + 12.25 = 0$

$x^{2} + y^{2} + 11 x - 3 y = - 12.25 (x^{2} + 11 x + {(\frac{11}{2})}^{2}) + (y^{2} - 3 y + {(- \frac{3}{2})}^{2}) = - 12.25 + {(\frac{11}{2})}^{2} + {(- \frac{3}{2})}^{2} {(x + 5.5)}^{2} + {(y - 1.5)}^{2} = 20.25 {(x + 5.5)}^{2} + {(y - 1.5)}^{2} = {(4.5)}^{2}$

Say What You Know

In your own words, talk about what you have learned using the objectives for this lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

Write the equation of a circle with the given information (graph, points).
Graph a circle from the given information.
Transform circles.