Find the equation of a straight line passing through the point (4, 5) and equally inclined to the lines `3x = 4y + 7 and 5y = 12x+6`.

The equation of the straight line passing through the point (3,2) and perpendicular to the line y=x is,

Find the equation of the straight line passing through the point (2,1) and through the point of intersection of the lines x+2y = 3 and 2x-3y=4

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 .

The equations of the lines which pass through the point (3, -2) and are inclined at 60° to the line sqrt(3) x + y = 1 is

Find the combined equation of the straight lines passing through the point (1,1) and parallel to the lines represented by the equation . x^2-5xy+4y^2+x+2y-2=0 .

Find the equation of a circle passing through the point (7,3) having radius 3 units and whose centre lies on the line y = x -1.

Find the vector equation of the line passing through the point (1,2,-4) and perpendicular to the two lines (x-8)/(3) = ( y +19)/(-16) = (z-10)/(7) and (x-15)/(3) = (y-29 )/(8) = (z-5)/(-5)

Find the vector equation of the line passing through the point (1,2,-4) and perpendicular to the two lines (x-8)/(3) = ( y +19)/(-16) = (z-10)/(7) and (x-15)/(3) = (y-29 )/(8) = (z-5)/(-5)

Find the equation of the line passing through (1,2,3) and parallel to the planes x-y+2z -5 =0 and 3x +y + z - 6 =0 .