Functions College Algebra Chapter 7 Points P x y the point P with coordinates x y A rational Curve a plane algebraic curve f x y 0 is rational if it can be parameterized by rational functions This means two rational functions x u t y v t such that at least one of u t v t is not a constant and f u t v t is identically zero This means we are parameterizing curves note all curves are not straight y mx b y ax2 bx c x h 2 y k 2 r2 Formula Circles Formula for Circle centered at the origin x y r 2 2 2 Center point 0 0 Radius r r 0 0 r r r x y 25 2 2 Center 0 0 Radius 5 Plot the center Count Plot the radius in 4 directions 0 5 5 0 0 0 5 0 0 5 x y 15 2 2 Center 0 0 Radius sqrt 15 Plot the center Count Plot the radius in 4 directions 0 3 9 3 9 0 0 0 3 9 0 0 3 9 x 2 y 5 6 25 2 2 Center 2 5 Radius 2 5 x 3 y 3 36 2 2 Center 3 3 Radius 6 x 2 y 4 121 2 2 Center 2 4 Radius 11 x 7 y 1 100 2 Center 7 1 Radius 10 2 If you expand the equation does it change the shape x 7 2 y 1 2 100 x2 14x 49 y2 2y 1 100 x2 14x y2 2y 100 49 1 x2 14x y2 2y 50 Can you work backwards x2 4x y2 8y 101 x2 4x y2 8y 101 but remember if you add to one side of an equation you must add to the other x2 4x y2 8y 101 how do you fill in the blanks to get an equation for a circle x h 2 y k 2 r2 x 4x y 8y 101 2 2 x2 4x y2 8y 101 x2 4x 2 y2 8y 4 101 4 16 can you make the connection from the left side to the right x h 2 y k 2 r2 x 2 2 y 4 2 121 2 2 CV 14 circle centered at P h k tangent to L So what is the process You have a line and a point Identify the slope and the perpendicular slope Identify the perpendicular line through the given point Find the point of intersection of the two lines Find the distance between the two points CV 9 Pythagorean Theorem a2 b2 c2 a2 c2 b2 a2 b2 c2 0 Find the equation of the circle
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