Question

(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 = ?

Answer 1

( 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