# What is the equation of a circle of radius 1, which is also tangent to the line 3x-4y+1=0 at the y-axis value = 1 ?

##### 1 Answer

There are two possible circles, either side of the line:

#### Explanation:

When

So the circle is tangential to the line at

Starting with

Divide both sides by

The slope of this line is

So this perpendicular line will have equation:

The centre of the tangential circle lies at distance

That give two possibilities:

and

...using the right angled property of the 3, 4, 5 triangle.

The corresponding circles have equations:

graph{(3x-4y+1)((x-2/5)^2 + (y-9/5)^2 - 1)((x-8/5)^2 + (y - 1/5)^2 - 1) = 0 [-3.52, 6.48, -1.28, 3.72]}