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 $\left( \frac { 1 } { 2 } , \frac { - \sqrt { 3 } } { 2 } \right)$ .

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The Answer of 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 $\left( \frac { 1 } { 2 } , \frac { - \sqrt { 3 } } { 2 } \right)$ .

Let L(x,y)=ax+byL ( x , y ) = a x + b yL(x,y)=ax+by

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