Intersection of a line and circle

[bosonhiggs]

Homework Statement

The line x+y=2a-1 intersects the circle x²+y²=a²+3a-3 at point (m,n). When m*n reaches its minimum value, what is the value of a?

Homework Equations

Equation One

x + y = 2a - 1

Equation Two

x² + y ² = a ² + 3a - 3

 

[uart]

Square your linear (first) equation, using the fact that (x+y)^2 = x^2 + y^2 + 2xy, at which point you can easily eliminate "x^2 + y^2" from the two equations. Now you have "xy" as a function of "a" and the rest should be easy.