Two equations and their graphs are given Find the intersecti

Two equations and their graphs are given. Find the intersection points of the graphs by solving the system. {x^2 + y^2 = 9x x = y^2 (x, y) () (smallest y-value) (x, y) = () (x, y) = () (largest y-value)

Solution

x^2 + y^2 = 9x

x = y^2

plugging y^2 = 9x - x^2 from equation 1

x = 9x - x^2

bringing all terms on one side and making right side equal to 0

x^2 - 9x + x = 0

x^2 - 8x = 0

x ( x - 8 ) = 0

x = 0 , x = 8

y = 0 , y = +- sqrt 8

solutions are

( 8 , - sqrt 8 ) smallest y value

( 0 , 0 )

( 8 , + sqrt 8 ) largest y value