JEE Class main Answered

The straight line perpendicular to the line 7x+24y+15 = 0 is  24x-7y +c = 0 , where ci sconstannt.

If the perpendicular line  ( 24x - 7y + c ) = 0 is passing through origin ,

then equation of this line is 7y  = 24x as shown in figure.

Point of intersection is obtained by substituting y = (24/7) x  in the equation 7x+24y+15 = 0 .

7x + 24 (24/7) x + 15 = 0

625 x + 105 = 0

hence we get x = - 0.168 from above expression

if point P is on the line " 7y = 24 x " , then  y = -0.576

Hence distance OP which is perpendicular distance from origin to line 7x+24y+15 = 0  is