# What is the equation of a circle that has its center at the origin and is tangent to the line with equation 3x-4y=10?

##### 1 Answer

The circle's equation would be

#### Explanation:

We know that a circle's equation centered at the origin would look something like

We can make a system of equations:

We can solve for

We can put this into the second equation:

Now we have to think a little. The word "tangent" in the question would mean that the system of equations has one solution for

In order for a quadratic to have exactly one solution (and not two or zero), the discriminant has to be

Setting the discriminant equal to

We found the radius! We can now write the equation of the circle:

That's the solution. Hope this helped!