How do you find all possible equations for a circle that lies on the line 3x + y = 6, has a radius of 4, and is tangent to the y-axis?

Question

You have to list all possible equations that fit those descriptions.

Answer 1

Draw and label a diagram!

The circle does not fit in QI - the line is less than 4 units from the y-axis.

The circle can be in QII or QIV.

To be tangent to the y-axis and have a radius of 4 the x value of the center must be either - 4 or +4.

Substitute both into the given equation to determine the value of y.

Substitute values into the appropriate formula of a circle.