Sample QuestionsPART - 2 CH - 9 Straight Lines questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The equation of line passing through point of intersection of lines $a x+2 b y+3 b=0$ and $b x-2 a y$ $-3 a=0$ and parallel to $x$-axis, while $(a, b \neq 10,0)$ is :
- A
Above $x$-axis and is at a distance of $\frac{3}{2}$ units
- B
Above $x$-axis and is at a distance of $\frac{2}{3}$ units
- ✓
Below $x$-axis and is at a distance of $\frac{3}{2}$ units
- D
Below $x$-axis and is at a distance of $\frac{2}{3}$ units.
Answer: C.
View full solution →If line passing through point $(4,3)$ and $(2, k)$ is perpendicular to the line $y=2 x+3$, then $k$ equals to :
Answer: C.
View full solution →The image of point $(3,8)$ in line $x+2 y-7=0$ is given by:
- A
$(-1,-4)$
- ✓
$(-3,-8)$
- C
$(1,-4)$
- D
$(3,8)$
Answer: B.
View full solution →If lines $a_1 x-b_1 y+c_1=0$ and $a_2 x+b_2 y+c_2=0$ are mutually perpendicular then :
- A
$a_1 b_2+a_2 b_1=0$
- B
$a_1 a_2+b_1 b_2=0$
- C
$a_1 b_2-a_2 b_1=0$
- ✓
$a_1 a_2-b_1 b_2=0$
Answer: D.
View full solution →The length of perpendicular drawn from origin $(0,0)$ to line $x \sec \theta+y \operatorname{cosec} \theta=a$ is given by :
- ✓
$a \sin \theta \cos \theta$
- B
$a \cos \theta \operatorname{cosec} \theta$
- C
$a \operatorname{cosec} \theta \sec \theta$
- D
$a$
Answer: A.
View full solution →Equation of line perpendicular to line $a x+b y+c=0$ is given by $b x+a y+\lambda=0$, where $\lambda$ is a constant.
View full solution →The distance of point $\left(x_1, y_1\right)$ from line $a x+b y+c=$ 0 is given by
$d=\frac{a x_1+b y_1+c}{\sqrt{a^2+b^2}}$
View full solution →Equation of line passing through points ( $\left.x_1, y_1\right)$ and $\left(x_2\right.$, $\left.y_2\right): y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$
View full solution →Equation of line passing through point $\left(x_1, y_1\right)$ having slope $m$ is given by $y-y_1=m\left(x-x_1\right)$.
View full solution →Equation of line perpendicular to $x$-axis and at a distance $b$ unit from y-axis $x=b$ or $x=-b$.
View full solution →Write the equation of line passing through point ( -4 , -3 ) and parallel to $x$-axis.
View full solution →Find the equation of line perpendicular to line $3 x-5 y$ $+7=0$ and passing through point $(1,5)$.
View full solution →Find the distance between the parallel lines $3 x-4 y+$ $2=0$ and $6 x-8 y+3=0$.
View full solution →Find the distance between parallel lines $2 x+3 y+4$ $=0$ and $2 x+3 y-2=0$.
View full solution →Find the length of the perpendicular drawn from point $(4,5)$ on line $y=m x+c$.
View full solution →Find the equation of a line passing through point of intersection of lines $2 x+y=5$ and $x-2 y=$ 0 which makes an angle $45^{\circ}$ with $x$-axis.
View full solution →Prove that lines $7 x-5 y+20=0$ and $5 x+7 y+$ $19=0$ are mutually perpendicular to each other.
View full solution →Prove that perpendiculars drawn from any point taken on line $7 x+4 y=3$ to the lines $3 x-4 y=$ 2 and $5 x-12 y=4$ are equal in length.
View full solution →Find the equation of straight lines which passes through point of intersection of lines $y-3 x+5$ $=0$ and $y-2 x+2=0$ and is at a distance of $7 / \sqrt{2}$ unit from origin.
View full solution →Find the equation of the straight line which joints the point $(3,5)$ to the point of intersection of lines $4 x+y=1$ and $7 x-3 y-35=0$. Prove that this line is at equal distance from origin and point $(8,34)$.
View full solution →Find the image of point $(2,3)$ w.r.t. line $x-2 y+$ $1 = 0$.
View full solution →Find the distance of point $(1,2)$ from straight line $3 x+y+4=0$, when it is drawn parallel to line $3 x-4 y+8=0$.
View full solution →The equation of $x$-axis is. _____________
View full solution →The distance between lines $Ax + B y+ C _1=0$ and $A x$ $+ B y+ C _2=0$ is _____________
View full solution →If two lines are mutually perpendicular, then their slopes are _____________
If lines $l_1$ and $l_2$ are parallel then their slopes are _____________
View full solution →The slope of $x$-axis is _____________
View full solution →| Part (A) | Part (B) |
| 1. The slope of line passing through points $(3,-5)$ and $(1,2)$ | (a) $x=2$ |
| 2. Equation of line parallel to $x$-axis and passing through point $(3,-5)$ | (b) $-\frac{7}{2}$ |
| 3. Equation of line parallel to $x$-axis and is at equal distance from lines $x=-2$ and $x=6$ | (c) $y=2 x+3$ |
| 4. Equation of line having slope 2 and which cuts $y$-intercept as 3 . | (d) $y=-5$ |
| 5. Equation of line passing through point $(6,2)$ having slope -3 | (e) $3 x+y-20=0$ |
| Part (A) | Part (B) |
| 1. The angle between the lines$2 x-y+3=0$ and $x+2 y+3=0$ | (a) $-\frac{7}{2}$ |
| 2. The image of point $(4,-13)$ in line $5 x+y+6=0$ | (b) $(-1,-14)$ |
| 3. Point at equal distance from lines $4 x+3 y-10-0$, $5 x-12 y+26=0$ and $7 x+24 y-50=0$ | (c) $90^{\circ}$ |
| 4. If slope of line passing through points $(2,5)$ and $(x, 3)$ is 2 , then the value of $x$ is | (d) $(0,0)$ |
| 5. The slope of line passing through points $(3,-5)$ and $(1,2)$ | (e) 1 |