Nellie is analyzing a circle, y2 + x2 = 25, and a linear function g(x). Will they intersect? y2 + x2 = 25 g(x) graph of the function y squared plus x squared equals 25 x g(x) −7 −2 −6 −1 1 6
Accepted Solution
A:
The linear function is given by the following table: -7 -2 -6 -1 1 6 The equation of the line is: y = x + 5 The equation of the circle is: y2 + x2 = 25 Therefore we have the following system of equations: y2 + x2 = 25 y = x + 5 The solution is: x = -5, y = 0 x = 0, y = 5 Therefore, the line and the circle intersect at two points: (-5, 0) (0, 5) Answer: they will intersect at: (-5, 0) (0, 5)