Show that the lines x+7y=23 and 5x+2y=16 interest at the point (2,3)

Which of the lines 2 x+7 y-9=0 and 4 x-y+11=0 is farther from the point (2,3) ?

Show that the line x - 7y + 5 = 0 is a tangent to the circle x^2+y^2-5x+5y=0 . Find the point of contact. Find also the equation of tangent parallel to the given line.

Prove that the points of intersection of the line x-y=2 with the parallel lines 2x+y=7 and 2x+y=16 are on the opposite sides of the line x+y=5 .

Prove that the points of intersection of the line x-y=2 with the parallel lines 2x+y=7 and 2x+y=16 are on the opposite sides of the line x+y=5 .

Find the equation of a line passing through the point of intersection of the lines 3x+5y=-2 and 5x-2y=7 and perpendicular to the line 4x-5y+1=0 .

Find the equation of a line passing through the point of intersection of the lines 3x+5y=-2 and 5x-2y=7 and perpendicular to the line 4x-5y+1=0 .

Prove that the three lines 5x+3y-7=0, 3x-4y=10, and x+2y=0 meet in a point.

Show that the line y =x + sqrt7 touches the hyperbola 9x ^(2) - 16 y ^(2) = 144.

Show that the lines 2x+y-3=0,3x+2y-2=0 and 2x-3y-23=0 are concurrent and find the point of concurrency.

Show that the points (2,3,-5) and (3,4,7) lie on the opposite side of the plane x+2y-2z=9