Show that the pair of lines represented by x^2 - 4xy - 5y square = 0 are parallel to the pair of lines represented by x^2 - 4xy - 5y^2 - 2 x - 2y = 0



Answer :

Answer:To show that the two pairs of lines are parallel, we need to show that they have the same slope.

The first pair of lines is represented by:

x^2 - 4xy - 5y^2 = 0

This can be factored as:

(x - 5y)(x + y) = 0

Which gives us two lines:

x - 5y = 0 --> y = (1/5)x

x + y = 0 --> y = -x

The slopes of these lines are 1/5 and -1, respectively.

The second pair of lines is represented by:

x^2 - 4xy - 5y^2 - 2x - 2y = 0

This can be rearranged as:

x^2 - 4xy - 5y^2 = 2x + 2y

Subtracting 2x + 2y from both sides gives us:

x^2 - 4xy - 5y^2 - 2x - 2y = 0

Factoring the left-hand side gives us:

(x - 5y)(x + y) = 2(x + y)

Which gives us two lines:

x - 5y = 0 --> y = (1/5)x

x + y = 2 --> y = -x + 2

The slopes of these lines are also 1/5 and -1, respectively.

Since the slopes of the lines in both pairs are the same, the pairs of lines are parallel.

Step-by-step explanation: