1 College Algebra Chapter 7 • P(x,y)–the point P with coordinates (x,y) • a plane algebraic curve f(x, y) = 0• is rational if it can be parameterized by rational functions.2 • 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. • note all curves are not straight• y = mx + b• y = ax2+ bx + c• (x-h) 2+ (y-k) 2= r2 3Formula for Circle centered at the originCenter point (0,0)Radius = r(0,0)rrrr• Center = (0,0)• Radius = 5• Plot the center• Count & Plot the radius in 4 directions4(0,0)(0,5)(0,-5)(5,0)(-5,0)• Center = (0,0)• Radius = sqrt(15)• Plot the center• Count & Plot the radius in 4 directions (3.9,0)(-3.9,0) (0,0)(0,3.9)(0,-3.9)5• Center = (2,5)• Radius = 2.5!"#!"#$%• Center = (3,3)• Radius = 6!"&#!"&#&$• Center = (-2,-4)• Radius = 11!#!'# 6• Center = (-7,1)• Radius = 10!(#!" # ))(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*+ ,- , .• x2+4x+y2+8y = 101• x2+4x+ +y2+8y+ = 101101• 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 /0/ ,.7• x2+4x+ +y2+8y+ = 101101• x2+4x+ +y2+8y+ = 101 + +• can you make the connection from the left side totothe right?• (x – h)2+ (y – k)2= r2• (x + 2)2+ (y + 4)2= 121'1 ) 22224444221616CV # 14 ,!2/# 384 • 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 # 99 • a2+ b2= c2• a2= c2- b2• a2+ b2- c2 = 0 ,-
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