Question

Show that the pairs of lines 6x2 – 5xy – 6y2 = 0, 6x2 – 5xy – 6y2 + x + 5y – 1 = 0 form a square.

Answer 1

Given pairs of lines are 6x2 – 5xy – 6y2 = 0 ........ (1)

6x2 – 5xy – 6y2 + x + 5y – 1 = 0 ........ (2)

Equation (1) represents a pair of perpendicular lines passing through the origin and Eq. (2) represents a pair of perpendicular lines parallel to (1)

⇒ Diagonals of the rectangle OABC are perpendicular

⇒ OABC is a square.