Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation. \( \mathrm{r}=7 \)

To transform the polar equation \( r = 7 \) into an equation in rectangular coordinates, we use the relationships between polar and rectangular coordinates: \[ x = r \cos(\theta) \] \[ y = r \sin(\theta) \] Since \( r = 7 \) is a constant, we can square both sides to get: \[ r^2 = 7^2 \] \[ x^2 + y^2 = 49 \] This is the equation of a circle in rectangular coordinates with its center at the origin (0, 0) and a radius of 7 units. To graph this equation, you would plot a circle with the following characteristics: - Center: (0, 0) - Radius: 7 units Here's a simple way to visualize the graph: ``` y ^ | | * | * | * | * | * |*------------------*------------------* x ``` The circle is centered at the origin and extends 7 units in all directions along the x and y axes.