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?
Let the coordinate of the center of the circle lying on x-axis 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.
Putting this value of a =6 in (2) we get
Now finally plugging in the value of