Topics

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

Correct Answer:
B) \( \Large \left(-\frac{1}{3},\ \frac{1}{3}\right) \)

Description for Correct answer:

Set of lines passes through intersection point of

\( \Large x-2y+1=0\ and\ x+y=0 \) which  is \( \Large \left(-\frac{1}{3},\ \frac{1}{3}\right) \)


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




Comments
No comments available




Similar Questions
1). 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
-- View Answer
2). 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
-- View Answer
3). 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
-- View Answer
4). 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
-- View Answer
5). 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
-- View Answer


6). 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
-- View Answer
7). 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). \( \Large \sqrt{3}y-x+2\sqrt{3}=0 \)
-- View Answer
8). 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). \( \Large a=1,\ b=1,\ c=1 \)
-- View Answer
9). The line parallel to the x-axis and passing through the intersection of the lines \( \Large ax+2by+3b=0\ and\ bx-2ay-3a=0 \), where \( \Large (a, b) \ne (0, 0) \), is
A). above the x-axis at a distance of \( \Large \frac{2}{3} \) from it.
B). above the x-axis at a distance of \( \Large \frac{3}{2} \) from it.
C). below the x-axis at a distance of \( \Large \frac{2}{3} \) from it.
D). below the x-axis at a distance of \( \Large \frac{3}{2} \) from it.
-- View Answer
10). The number of integral values of m, for which the x-coordinate of the point of intersection of the line \( \Large 3x+4y=9\ and\ y=mx+1 \) is also an integer is:
A). 2
B). 0
C). 4
D). 1
-- View Answer
Home About Us Terms and Conditions Privacy Policy Contact us