Provide an Appropriate Response $x ^ { 2 } + y ^ { 2 } < 3 x + y$

Essay

Provide an appropriate response.
-Consider the inequality $x ^ { 2 } + y ^ { 2 } < 3 x + y$ .
(a) Find an equivalent inequality in polar coordinates.
(b) Use an integral with respect to $\theta$ to find the area of the region defined by the inequality.
(c) Find the length of the curve that forms the boundary of the region defined by the inequality.
(d) Find the slope of this curve at the point $( 2,2 )$ .