Chapter 1.8 Coordinate plane

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

• Notes
• 55

This preview shows page 48 - 53 out of 55 pages.

The circle’s center is (4 , - 5) and its radius is 7 . Stanley Ocken M19500 Precalculus Chapter 1.8: The Coordinate Plane

Subscribe to view the full document.

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
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

Subscribe to view the full document.

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
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?

Subscribe to view the full document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern