Let $L ( x , y ) = a x + b y$

Essay

Let $L ( x , y ) = a x + b y$ .Find values of a and b so that $L ( x , y )$ takes a maximum value of 4 on the unit circle $x ^ { 2 } + y ^ { 2 } = 1$ at the point $\left( \frac { 1 } { 2 } , \frac { - \sqrt { 3 } } { 2 } \right)$ .