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

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

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

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Answer 1 · 2017-10-09T10:39:05

See below.

Explanation:

Assuming that the formula reads $a x^{2} + 6 x y + y^{2} + b x + c y + d = 0$ $ax^2+6xy+y^2+bx+cy+d=0$

Given that $(y + m x + c_{1}) (y + m^{2} x + c_{2}) = a x^{2} + 6 x y + y^{2} + b x + c y + d = 0$ $(y+m x+c_1)(y+m^2 x+c_2) = ax^2+6xy+y^2+bx+cy+d=0$

we have comparing coefficients.

$a = m^{3}$ $a = m^3$ and

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

then

$a$ $a$ can assume the values $- 27, 8$ $-27,8$

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

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

1 Answer

Explanation:

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If the equation ax2−6xy+y2+bx+cy+d=0ax^2-6xy+y^2+bx+cy+d=0 represents a pair of straight lines whose slopes are mm and m2m^2, then value(s) of a is/are?

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

1 Answer

Explanation:

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Impact of this question

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

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