How do you write the standard equation of a circle with the given center (-4,3) and tangent to the line y=1?
The center is already given, so the remaining item to obtain is the radius
The circle is tangent to the line
We can get the radius by obtaining the distance between the center and point of tangency.
The point of tangency is at
Get the point of tangency by getting the intersection of the line passing through both the center and the point of tangency, and the tangent line.
Remember that the these lines are perpendicular. So the slope of one line should be equal to the negative inverse of the other.
Since the tangent line is
Since this line should pass through the center
Getting the intersection should yield us
Now lets get the distance between the center and the point of tangency. This distance should be equal to the radius