Question

Equations of pairs of opposite sides of a parallelogram are x² - 7x + 6 = 0 and y² - 14y + 40 = 0. Find the joint equation of its diagonals.

Answer 1

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.

Now you have all the four coordinates ..now find equstions of diagonals

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

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