The lines `x-2y+6=0 and 2x-y-10=0` intersect at P. Without finding the co-ordinate of P prove that the equation of the line through P and the origin of co-ordinates is perpendicular to `39x+33y-580=0`.

The line 4x - 3y + 12 = 0 meets x-axis at A. Write the co-ordinates of A. Determine the equation of the line through A and perpendicular to 4x - 3y + 12 = 0 .

Find the equation of the line through the intersection of y+x=9 and 2x-3y+7=0 , and perpendicular to the line 2y-3x-5=0 .

The line segment joining the points A (3,-4) and B (-2, 1) is divided in the ratio 1:3 at point P in it. Find the co-ordinates of P. Also, find the equation of the line through P and perpendicular to the line 5x – 3y = 4 .

A line 5x + 3y + 15 = 0 meets y-axis at point P. Find the co-ordinates of point P. Find the equation of a line through P and perpendicular to x - 3y + 4 = 0 .

Find the equation of the line through the intersection of y+x=9 and 2x-3y+7=0 , and perpendicular to the line 2y-3x-5=0

Find the equation of the line through the intersection of 5x-3y=1 and 2x-3y -23= 0 and perpendicular to the line 5x - 3y -1 =0 .

If the lines 2x+3y+1=0, 6x+4y+1=0 intersect the co-ordinate axes in 4 points, then the circle passing through the points is

Point P divides the line segment joining the points A (8,0) and B (16, -8) in the ratio 3:5. Find its co-ordinates of point P. Also, find the equation of the line through P and parallel to 3x + 5y = 7 .

Find the co-ordinates of the point of intersection of the straight lines 2x-3y-7=0 , 3x-4y-13=0