SOLUTION: What is the equation of the circle with center at (0, 2) and tangent to the line 3x - 4y = 12

All you need is to find the radius of the circle, i.e. the distance from the point (0,2) 
to the given straight line  3x - 4y - 12 = 0.


There is a remarkable formula which ideally suits for this need.


    Let the straight line in a coordinate plane is defined in terms of its linear equation 

         a*x + b*y + c = 0,

    where "a", "b" and "c" are real numbers, and let P = (,) be the point in the coordinate plane. 

    Then the distance from the point P to the straight line is equal to

        d = .


Regarding this formula, see the lesson
    The distance from a point to a straight line in a coordinate plane
in this site.


Substitute the given data  a= 3, b= -4, c= -12,   = 0,  = 2  into the formula to get the distance under the question


     =  =  = 4.


Answer.  The radius of the circle is 4 units.

         The standard equation of the circle is   +  = .