If the equation ax^2-6xy+y^2+bx+cy+d=0 represents a pair of straight lines whose slopes are m and m^2, then value(s) of a is/are?

A) a=-8
B) a=8
C)a=27
D)a=-27

1 Answer
Oct 9, 2017

See below.

Explanation:

Assuming that the formula reads ax^2+6xy+y^2+bx+cy+d=0

Given that (y+m x+c_1)(y+m^2 x+c_2) = ax^2+6xy+y^2+bx+cy+d=0

we have comparing coefficients.

a = m^3 and

6 = m+m^2 and solving we obtain m = {-3,2}

then

a can assume the values -27,8