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Separate equations of lines for a pair of lines whose equation is \( \Large x^{2}+xy-12y^{2}y^{2}=0 \), are

A) \( \Large x+4y=0\ and\ x+3y=0 \)
B) \( \Large x+4y=0\ and\ x-3y=0 \)
C) \( \Large x-6y=0\ and\ x-3y=0 \)
D) \( \Large 2x-3y=0\ and\ x-4y=0 \)

Correct Answer:


B) \( \Large x+4y=0\ and\ x-3y=0 \)

Description for Correct answer:

Given equation can be rewritten

\( \Large x^{2}+4xy-3xy-12y^{2}=0 \)

Factorising the above equation we get

\( \Large \left(x+4y\right) \left(x-3y\right)=0 \)

Therefore separate equations for the lines are

\( \Large x+4y=0\ and\ x-3y=0 \)

Part of solved Straight lines questions and answers : >> Elementary Mathematics >> Straight lines

Comments

Similar Questions

1). The equation \( \Large 12x^{2}+7xy+ay^{2}+13x-y+3=0 \) represents a pair of perpendicular lines. Then the value of 'a' is:

A). \( \Large \frac{7}{2} \)

B). -19

C). -12

D). 12

2). If the \( \Large \angle \theta \) is acute, then the acute angle between \( \Large x^{2} \left(\cos \theta -\sin \theta \right)+2xy \cos \theta +y^{2} \left(\cos \theta +\sin \theta \right)=0 \) is

A). \( \Large 2 \theta \)

B). \( \Large \frac{ \theta }{3} \)

C). \( \Large \theta \)

D). \( \Large \frac{ \theta }{2} \)

3). The equation \( \Large 2x^{2}-24y+11y^{2}=0 \) represents:

A). two parallel lines

B). two lines passing through the origin

C). two perpendicular lines

D). a circle.

4). Lines \( \Large 2x+y=1\ and\ 2x+y=7 \) are

A). on the same side of a point \( \Large \left(0,\ \frac{1}{2}\right) \)

B). on the Opposite side of a point \( \Large \left(0,\ \frac{1}{2}\right) \)

C). same lines

D). perpendicular lines.

5). Set of lines \( \Large \left(x-2y+1\right)+h \left(x+y\right)=0 \) (where h is a parameter) passing through a fixed point:

A). \( \Large \left(\frac{1}{3},\ -\frac{1}{3}\right) \)

B). \( \Large \left(-\frac{1}{3},\ \frac{1}{3}\right) \)

C). (1, 1)

D). none of these

6). The equation of the line equidistant from the lines \( \Large 2x+3y-5=0\ and\ 4x+6y=11 \) is

A). \( \Large 2x+3y-1=0 \)

B). \( \Large 4x+6y-1=0 \)

C). \( \Large 8x+12y-1=0 \)

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7). The equation of line parallel to lines \( \Large L_{1}=x+2y-5=0\ and\ x+2y+9=0 \) and dividing the distance between \( \Large L_{1} \) and \( \Large L_{2} \) in the ratio 1 : 6 (internally) is:

A). \( \Large x+2y-3=0 \)

B). \( \Large x+2y+2=0 \)

C). \( \Large x+2y+7=0 \)

D). none of these

8). The family of lines making an angle \( \Large 30 ^{\circ} \) with the line \( \Large \sqrt{3}y=x+1 \) is:

A). \( \Large x=h \) (h is parameter)

B). \( \Large y=-\sqrt{3}x+h \) (h is parameter)

C). \( \Large y=\sqrt{3}+h \)

D). none of these

9). A square of area 25 sq unit is formed by talking two sides as \( \Large 3x+4y=k_{1}\ and\ 3x+4y=k_{2} \) then \( \Large |k_{1}-k_{2}| \) is:

A). 5

B). 1

C). 25

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10). The lines \( \Large ax+by+c=0,\ bx+cy+a=0\ and\ cx+ay+b=0 \) \( \Large a \ne b \ne c \) are concurrent if:

A). \( \Large a^{3}+b^{3}+c^{3}+3abc=0 \)

B). \( \Large a^{2}+b^{2}+c^{2}-3abc=0 \)

C). \( \Large a+b+c=0 \)

D). none of these