The circles center is 4 5 and its radius is 7 stanley

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The circle’s center is (4 , - 5) and its radius is 7 . Stanley Ocken M19500 Precalculus Chapter 1.8: The Coordinate Plane
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The coordinate plane Equations and their graphs Finding points on graphs Circles Symmetry Quiz Review The method that you may have seen in high school is a bit longer but it involves exactly the same ideas. If you prefer to use it, see the following Example 12: Find the standard form equation, center, and radius of the circle with equation x 2 + y 2 = 8 + 8 x - 10 y Solution: x 2 + y 2 = 8 + 8 x - 10 y is the original equation. Rewrite it as x 2 - 8 x + y 2 + 10 y = 8 . Use completing the square to obtain x 2 - 8 x + ( ) + y 2 + 10 y + ( ) = 8 + ( ) + ( ) To fill in the first blank, use h = - 8 and so ( h/ 2) 2 = ( - 8 / 2) 2 = 16 . To fill in the second blank, use h = 10 and so ( h/ 2) 2 = (10 / 2) 2 = 25 . Now fill in the blanks on both sides to get x 2 - 8 x + (16) + y 2 + 10 y + (25) = 8 + (16) + (25) = 49 . Rewrite this as ( x - 4) 2 + ( y + 5) 2 = 7 2 , exactly as before. Answer: The standard form equation is ( x - 4) 2 + ( y + 5) 2 = 7 2 . The center is (4 , - 5) and the radius is 7 . Stanley Ocken M19500 Precalculus Chapter 1.8: The Coordinate Plane
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The coordinate plane Equations and their graphs Finding points on graphs Circles Symmetry Quiz Review Symmetry Start at either of the two points ( x, y ) and ( - x, y ) . If you draw a horizontal line to the y-axis, and then continue that line an equal distance past the y-axis, you arrive at the other point. We say that the two points are located symmetrically with respect to the y-axis. We also say that you have reflected the original point across the y-axis to obtain the second point. Definition A graph is symmetric with respect to the y-axis if reflecting any point on the graph across the y-axis yields another point on the graph. This will be the case provided replacing y by - y in that graph’s equation yields an equivalent equation (one with the same solutions). Stanley Ocken M19500 Precalculus Chapter 1.8: The Coordinate Plane
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The coordinate plane Equations and their graphs Finding points on graphs Circles Symmetry Quiz Review If you start with two points ( x, y ) and ( x, - y ) , copy over the last paragraph to see that each point is obtained from the other by reflection across the x-axis. Definition A graph is symmetric with respect to the x-axis if reflecting any point on the graph across the x-axis yields another point on the graph. This will be the case provided replacing y by - y in that graph’s equation yields an equivalent equation (one with the same solutions). From these statements its easy to see the following: Procedure To reflect the graph of an equation across the y-axis, substitute - x for x to obtain a new equation and draw the graph of that new equation. To reflect the graph of an equation across the x-axis, substitute - y for y to obtain a new equation and draw the graph of that new equation. Stanley Ocken M19500 Precalculus Chapter 1.8: The Coordinate Plane
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The coordinate plane Equations and their graphs Finding points on graphs Circles Symmetry Quiz Review Example 13: Is the graph of y = x + 7 x 3 + 8 x 5 x-axis symmetric?
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