Show that the line 3x=y+13 touches the circle and find the point of contact.
The centre of the given circle is (2,3) and radius is
The distance from the centre of the circle to the given line is
Now the perpendicular distance from the centre of the circle to the given line is equal to the radius of the circle. Hence the line touches the circle.
Let the point of contact be (x1,x2)
The distance between the centre and the point is equal to the radius.
The point lies on the given line,hence
Substituting this value in the above equation,we get
Hence the point of contact is (5,2)