# How do you write the standard equation of a circle with the given center (-4,3) and tangent to the line y=1?

##### 1 Answer

#### Answer:

#### Explanation:

The center is already given, so the remaining item to obtain is the radius

where

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