The product of lengths of the perpendiculars drawn from the point ( - 1 , 5 ) to the pair of lines 2 x 2 - x y - 3 y 2 + 6 x + y + 4 = 0 is

Step-by-step solution

Given: 2 x 2 - x y - 3 y 2 + 6 x + y + 4 = 0 First, we will find the separate equations. 2 x 2 - x y - 3 y 2 = 0 ⇒ 2 x 2 - x y + 2 x y - 2 x y - 3 y 2 = 0 ⇒ x + y 2 x - 3 y = 0 Now, m   &   l be the constants term in the above equations. x + y + m = 0 2 x - 3 y + l = 0 Then, 2 x 2 - x y - 3 y 2 + 6 x + y + 4 = x + y + m 2 x - 3 y + l On comparing the coefficients, we get l x + 2 m x = 6 x ⇒ l + 2 m = 6     . . . i l y - 3 m y = y ⇒ l - 3 m = 1     . . . i i