find the equation of the circle whose centre is (-3,1) and which cuts off an intercept of length 6 from the line 2x-5y+16=0

Step 1 : General Equation of circle is given by – x^2 + y^2 + 2gx + 2fy + c = 0 whose
Centre = (-g, -f) and Radius^2 = g^2 + f^2 + c

Step 2: given Centre = -3, 1 therefroe g = 3 and f = -1. Now to find c we will find radius^2.

Step 3: Find the perpendicular distance of Center to the given line. This Perpendicular line is the bisector for that line within the circle. Now using the Phythogorus theorem find the Radius^2 from here and equate it to the general relation of radius^2 from step 1 and get the value of c. And hence get the equation of circle.

Thanks,Vijay Mukati