Write the equation of each conic described below.

1. A circle whose center lies on the line $3x + y = 6$. The circle has a radius of $4$ and is tangent to the $y$-axis.

   Hint (a):

   The $x$-coordinate of the circle must be either $x = 4$ or $x = −4$. Why?

2. A parabola with the focus at $\left(3, 2\right)$ and a directrix of $x = −5$.

   Hint (b):

   This parabola opens to the left. Why?
   Sketch the situation to help locate the vertex and determine the value of $c$.

   More Help (b):

   Review the Math Notes box in Lesson 11.1.5.