# How do you write an equation for a circle tangent to the line x - y = 2 at the point (4,2) and the center is on the x-axis?

##### 1 Answer

#### Answer:

#### Explanation:

Let the coordinate of the center of the circle lying on x-axis be **The equation of the circle will be**

Now the point (4,2) is lying on the circle.So

Now it is given that

Witing the equation of the tangent in

Hence the slope of the normal passing through (4.2) is

So equation of the normal at (4,2) will be

Now as the center (a,0) is lying on the normal ,it will satisfy the equation of normal.

So inserting

Putting this value of a =6 in (2) we get

Now finally plugging in the value of