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?

Question

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

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Answer 1 · 2017-10-09T10:39:05

See below.

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#