Conditions for Parallel and Perpendicular Lines

Q. Given the linear equation $2x+3y-8=0$, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
(i) intersecting lines
(ii) parallel lines
(iii) coincident lines.

Q. If two lines are mutually perpendicular, then the product of the slopes of two lines will be:

Q.

Find the equation of a straight line whose y intercept is $-4$ and is parallel to the line joining the points $(3,-2)$ and $(1,4)$.

1. $x+3y+4=0$

2. $3x+y-3=0$

3. $x+3y-3=0$

4. $3x+y+4=0$

Q.

The equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0 is ______.

1. 2y - 3x = 0

2. 3y + 2x = 0

3. 2y + 3x = 0

4. 3y - 2x = 0

Q.

Two lines, with slopes 'm' and 'n', are parallel to each other if ______.

1. 1/m + 1/n = 1

2. mn=0

3. m=n

4. m+n=0

Q.

If the lines mx - ny + 5 = 0 and 2x + 3y + 6 = 0 are perpendicular to each other, then find the relation between m and n

1. $2m=3n$

2. $2m=n$

3. $m=3n$

4. $m=n$

Q.

The line joining the points $(8,2),(-5,3)$ is neither parallel nor perpendicular to the line passing through points $(16,6)$ and $(3,15)$.

1. False

2. True

Q.

The slope of a line passing through points $(1,2)$ and $(10,20)$ is ___.

Q.

Equation of the line passing through $(1,2)$ and parallel to the line $y=3x-1$ is

1. $y+1=3x$

2. $y=3(x-1)$

3. $y-2=3(x-1)$

4. $y=3x-1$

Q.

The slope of the line perpendicular to $x-\frac{y}{2}+3=0$ is _____.

1. $\frac{1}{2}$

2. $\frac{-1}{2}$

3. -2

4. 2

Q.

Find the equation of a line drawn perpendicular to the line $\frac{\mathrm{x}}{4}+\frac{\mathrm{y}}{6}=1$ through the point, where it meets the $Y-axis.$

Q. The equation of the line $y=\frac{2}{3}x-1$, passes through

1. $(0,1.5)$ and slope, $m=\frac{2}{3}$
2. $(1.5,0)$ and slope, $m=\frac{2}{3}$
3. $(0,1.5)$ and slope, $m=-\frac{2}{3}$
4. $(1.5,0)$ and slope, $m=-\frac{2}{3}$

Q.

If the lines $2y-a^{2}x=3$ and $2y-(4ax+1)=0$ are parallel, find the value of a.

1. 6

2. 8

3. 2

4. 4

Q. If the lines $(p+1)x+y=3$ and $3y-(p-1)x=4$ are perpendicular to each other, find $p$.

1. 1

2. 2

3. -1

4. -2

Q. The parabola $y=x^2+5x+6$ is intersected by the line $y=-\frac{1}{2}x+12$. What is the y-coordinate of the intersection closest to the x-axis?

1. $10$
2. $12$
3. $4$
4. $2$

Q. If A$(-1,8)$, B$(4,-2)$ and C$(-5,-3)$ are the vertices of a triangle, then the equation of the altitude through $(-1,8)$ is given as $ax+b=y$. Find the value of $a+b$.

Q.

(i) Lines 2x - by + 5 = 0 and ax + 3y = 2 are parallel to each other. Find the relation connecting a and b.
$\left[1Mark\right]$

(ii) Lines mx + 3y + 7 = 0 and 5x - ny - 3 = 0 are perpendicular to each other. Find the relation connecting m and n.

$\left[1Mark\right]$

Q. The equation to the line passing through the intersection of $\frac{x}{a}+\frac{y}{b}=1,\frac{x}{b}+\frac{y}{a}=1$, where $ab=a+b$ and $(1,2)$ is

1. $y=1$
2. $y=2$
3. $x=1$
4. $x=2$

Q. The equation of the diameter of the circle $3(x^2+y^2)-2x+6y-9=0$ which is perpendicular to line $2x+3y=12$ is

1. $3x-2y=3$
2. $3x-2y=9$
3. none of these
4. $3x-2y+1=0$

Q. Draw the graph of the pair of equations $2x+y=4$ and $2x-y=4$ write the vertices of the triangle formed by these lines and the y-axis .also find the area of this triangle.

Q. The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.

Q.

Find the value of k if PQ and RS are parallel, given P(1, 2), Q(4, 5) and R(3, 4), S(8, k).

1. -7

2. 9

3. 7

4. -9

Q.

Find the value of $x$ if the line passing through $(x,-3)$ and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).

1. -2

2. 3

3. -3

4. 2