The joint equation of two lines passing through (-2,3) and parallel to the bisectors of the angle between the co-ordinate axes is

Step-by-step solution

Angle bisectors of coordinate axes are y=x and y=-x , equivalently x-y=0 and x+y=0 . A line parallel to x-y=0 passing through (-2,3) must satisfy x-y+c₁=0 , yielding -2-3+c₁=0 , so c₁=5 . Thus, L₁: x-y+5=0 . Similarly, a line parallel to x+y=0 through (-2,3) satisfies x+y+c₂=0 , giving -2+3+c₂=0 , so c₂=-1 , and L₂: x+y-1=0 . The joint equation is (x-y+5)(x+y-1)=0 , which expands to x^2 - y^2 + 4x + 6y - 5 = 0 . This matches option C .