Find the equations of the circles passing through the point `(-4,3)` and touching the lines `x+y=2` and `x-y=2`

Find the equation of the circle passing through the point (4,1) and (6,5) and whose centre is on the line 4x + y = 16 .

Find the equation of the circle passing through the points (2,3) and (-1,-1) and whose centre is on the line x-3y-11=0.

Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre is on the line 4x+y=16 .

Write the equation of the line passing through the point (1,-1) and parallel to the line x+3y -4=0

Find the equation of the line passing through the point of intersection of the lines 4x + 7y - 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.

Find the equation of the circle which passes through the points (1,-2),(4,-3) and whose center lies on the line 3x+4y=7.