# How do you write the equation for a circle with center at (0, 0) and touching the line 3x+4y=10?

##### 1 Answer

#### Explanation:

To find the equation of a circle we should have the center and radius.

Equation of circle is:

Where (a,b) : are the coordinates of the center and

r :Is the radius

Given the center (0,0)

We should find the radius .

Radius is the perpendicular distance between (0,0) and the line 3x+4y=10

Applying the property of the distance

```
# d = |A*m+B*n+C| / sqrt(A^2+B^2)#
```

The radius which is the distance from straight line

A=3. B=4 and C=-10

So,

=

=

=

=

So the equation of the circle of center(0,0) and radius 2 is :

That is