Question

The equation - $8x^2$ - l4xy + $3y^2$ + 10x + 10y 25 = 0 represents two adjacent sides of a parallelogram whose diagonals intersect at the point (3, 2). Determine the equation of other two sides.

Answer 1

$8x^2$ - l4xy + $3y^2$ = (2x - 3y)(4x - y) Hence the factors of given expression are

$(2x-3y+p)(4x-y+q)$

Comparing coefficients, we get p = 5, q = -5

$\therefore$ AB and AD are

$2x-3y5=0$ and $4xy5=0$

and their point of intersection A is (2, 3). Again C is found, as P(3, 2) is mid-point of diagonal AC

$\therefore$ C is (4, 1). Now CD is parallel to AB and passes through C,

$\therefore$ CD is $2x-3y-5=0$. Similarly CB is $4x-y+15=0.$