Answer:
The equation of a pair of straight lines parallel to a given pair of lines can be found by adding a constant multiple of the given equation to itself.
Given equation is x²+2xy+y²-2x-2y-15.
To find the equation of the pair of lines parallel to this equation, we can add a constant multiple of the equation to itself.
so adding k(x²+2xy+y²-2x-2y-15) to x²+2xy+y²-2x-2y-15, we get
(1+k)x²+(2+2k)xy+(1+k)y²-(2+2k)x-(2+2k)y-(15+15k) = 0
As these lines pass through the origin so the equation will be
(1+k)x²+(2+2k)xy+(1+k)y² = 0
This is the equation of the pair of lines parallel to the lines represented by the equation x²+2xy+y²-2x-2y-15 and passing through the origin.