Find an equation of the plane consisting of all points that are equidistant from (0, -2, 0) and (4, -3, 0), and having 4 as the coefficient of x.

SOLUTION -  GIVEN = Two  Points  (0,-2,0) & (4, -3,0 ) which are inequidistant  

                                     from the all the points of plane.

                    Find out = Equation of plane

TO PROOF - The general equation of plane .

                      a ( x-x₀) + b ( y- y₀) + c(z-z₀) =0

                     let  A = (0,-2,0) & B = (4, -3, 0 )

 is orthogonal to plane and become the normal vector.)

               let O be midpoint

               O = ( 0+4, -2-3, 0-0 )

                  =\frac{1}{2} ( 4, -5, 0)

                 =

        Equation of the plane by using the point & normal vector

         by using general equation of a plane

           4 ( x- 2) -1 (y + = 0

        Hence Proved

were is the equation