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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.

Correct Answer:



C) two perpendicular lines

Description for Correct answer:
Given equation can be rewritten as

\( \Large 2x^{2}-22xy-2xy+11y^{2}=0 \)

=> \( \Large 2x \left(x-11y\right)-2y \left(x-11y\right)=0 \)

=> \( \Large \left(2x-2y\right) \left(x-11y\right)=0 \)

=> \( \Large 2x-2y=0\ or\ x-11y=0 \)

=> \( \Large y=x\ or\ y=\frac{x}{11} \)

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

Comments

Similar Questions

1). 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.

2). 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

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

D). none of these

4). 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

5). 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

6). 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

D). none of these

7). 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

8). A straight line through the point (2, 2) intersects the lines \( \Large \sqrt{3}x+y=0\ and\ \sqrt{3}x-y=0 \) at the points A and B. The equation to the line AB so that the triangle OAB is equilateral is:

A). \( \Large x-2=0 \)

B). \( \Large y-2=0 \)

C). \( \Large x+y-4=0 \)

D). none of these

9). Equation to the straight line cutting of an intercept from the negative direction of the axis of y and inclined at \( \Large 30 ^{\circ} \) to the positive direction of axis of x is:

A). \( \Large y+x-\sqrt{3}=0 \)

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

C). \( \Large y-\sqrt{3}x-2=0 \)

D). \( \Large \sqrt{3}y-x+2\sqrt{3}=0 \)

10). Two consecutive side of parallelogram are \( \Large 4x+5y=0\ and\ 7x+2y=0 \). One diagonal of the parallelogram is \( \Large 11x+7y=9 \) the other diagonal is\( \Large ax+by+c=0 \), then

A). \( \Large a=-1,\ b=-1,\ c=2 \)

B). \( \Large a=1,\ b=-1,\ c=0 \)

C). \( \Large a=-1,\ b=-1,\ c=0 \)

D). \( \Large a=1,\ b=1,\ c=1 \)