(Visual diagram of x^{2}+y^{2}=9)
Use the diagram to help you decide the maximum number of solutions possible if any linear equation and x^{2} + y^{2} = 9 are solved simultaneously.
Maximum number of solutions = ?
( x - a )² + ( y - b)² = r²
is the equation of a circle where:
a = x coordinate of the circle centre
b = y coordinate of the circle centre
r = the radius of the circle
x + y² = 9
This the equation of a circle with the center at the origin of the coordinate system ( points with coordinates: x = 0 , y = 0 ) and with the radius r = 3
A line and a circle may not have a common point where they touch, or one common point where they touch ( then the line is a tangent to the circle ), or two common points where they touch.
Maximum number of solutions = 2