27
MCQ (Single Correct Answer)
If the line $\frac{x}{a}+\frac{y}{b}=1$ passes through the points $(2,-3)$ and $(4,-5)$, then $(a, b)$ is
A
$(1,1)$
B
$(-1,1)$
C
$(1,-1)$
D
$(-1,-1)$
28
MCQ (Single Correct Answer)
The distance of the point of intersection of the lines $2 x-3 y+5=0$ and $3 x+4 y=0$ from the line $5 x-2 y=0$ is
A
$\frac{130}{17 \sqrt{29}}$
B
$\frac{13}{7 \sqrt{29}}$
C
$\frac{130}{7}$
D
None of these
29
MCQ (Single Correct Answer)
The equation of the lines which pass through the point $(3,-2)$ and are inclined at $60^{\circ}$ to the line $\sqrt{3} x+y=1$ is
A
$y+2=0, \sqrt{3} x-y-2-3 \sqrt{3}=0$
B
$x-2=0, \sqrt{3} x-y+2+3 \sqrt{3}=0$
C
$\sqrt{3} x-y-2-3 \sqrt{3}=0$
D
None of the above
30
MCQ (Single Correct Answer)
The equations of the lines passing through the point $(1,0)$ and at a distance $\frac{\sqrt{3}}{2}$ from the origin, are
A
$\sqrt{3} x+y-\sqrt{3}=0, \sqrt{3} x-y-\sqrt{3}=0$
B
$\sqrt{3} x+y+\sqrt{3}=0, \sqrt{3} x-y+\sqrt{3}=0$
C
$x+\sqrt{3} y-\sqrt{3}=0, x-\sqrt{3} y-\sqrt{3}=0$
D
None of the above
31
MCQ (Single Correct Answer)
The distance between the lines $y=m x+c_1$ and $y=m x+c_2$ is
A
$\frac{c_1-c_2}{\sqrt{m^2+1}}$
B
$\frac{\left|c_1-c_2\right|}{\sqrt{1+m^2}}$
C
$\frac{c_2-c_1}{\sqrt{1+m^2}}$
D
0