See the diagram.
Take a tangent to circle at P, which intercepts X axis at C(c,0) and y axis at D(0,d). Its equation is given by : c y + d x - cd = 0 It is simple that.
Area of triangle DOC is =
CPD is a tangent and its distance from origin is the radius = a.
Distance from O(0,0) to line cy+dx - cd = 0 is given by