# How do you write an equation of a circle whose center is at P(4,-5) and is tangent to the line -x+2y=1?

##### 2 Answers

#### Explanation:

Since the line is tangent to the circle, its distance from the center is equal to the radius, that's unknown:

d=r

where a,b,c are, in this case:

and

So

radius=

Now you can substitute the values in the equation of the circle:

#### Explanation:

Giving a circle

and a line

the tangency point

Their normal vectors are

so at tangency

The tangency point is obtained solving

Here we know

but

substituting the known values we obtain

we know that

so the circle is