The equations to a pair of opposite sides of a parallelogram are x^2-7x+6=0 and y^2-14y+40=0

Find the equations of diagonals

Hi Suhas,

From the Quad in x, you'll get (x-6)(x-1) = 0, or x=1 and x=6 are the equation of the sides.

From the other Quad in y, (y-10)(y-4)=0, y=4 and y=10 are the two equations.

So find the eqn of the diagonals passing through (1,4);(6,10)

The other diagonal will pass through (6,4);(1,10)

So that would solve the problem.

Best Regards,

Ashwin (IIT Madras).

If you factorise the given equations you will get x=6,x=1,y=4 and y=10(see in the image).Clearly the opposite points are (1,4) & (6,10) and (6,4) & (1,10).Then you can dind the eq. of diagonals by using Two-point form of a st. line.The eq. of diagonals are 6x - 5y + 14 = 0  and  6x + 5y - 56 = 0.