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QUESTION: 1

Which of the following lines is parallel to the line with equation 2x+y=3?

Solution:

This question can be done by picking the options.

a_{1}/a_{2} = b_{1}/b_{2} = c_{1}/c_{2}

Equation : 2x + y = 3

(d) 4x + 2y = 6

a_{1} = 2⇒, b_{1} = 1, c_{1} = 3

a_{2} = 4, b_{2} = 2, c_{2} = 6

⇒ 2/4 = 1/2 = 3/6

=> 1/2 = 1/2 = 1/2

QUESTION: 2

The equation of the line having normal distance 2a from the origin and angle 60° which the normal makes with the positive direction of X-axis is:

Solution:

We know that, If p is the length of the normal from origin to a line and w is the angle made by the normal with the positive direction of x-axis then the equation of the line is given by xcosw + ysinw = p.

Here, p=2a units and w=60°

Thus, the required equation of the given line is

xcos30° + ysin30° = 2a

x(1/2) + y(√3/2) = 2a

x + √3y = 4a

QUESTION: 3

The equation of a line with x intercept 4 and y intercept 3 is given by

Solution:

QUESTION: 4

Find the equation of the line whose intercepts on X and Y-axes are a^{2} and b^{2 }respectively

Solution:

Consider the given points. (a^{2},0) and (0,b^{2})

We know that the equation of the line which is passing through the points

y−y_{1} =[ (y_{2}−y_{1}) / (x_{2}−x_{1})] (x−x_{1})

So, y−0 = b^{2}−0/0-a^{2}(x-a^{2})

-ya^{2} - b^{2}x = -b^{2}a^{2}

xb^{2} +ya^{2} = b^{2}a^{2}

QUESTION: 5

The equations of the line parallel to X-axis and at a distance of c/2 from the X-axis is:

Solution:

The equation of straight line is parallel to x-axis which means slope is 0

equation of straight line , y = mx + c

here, m = 0 , y = c

As it is given c = c/2

y = +-c/2

QUESTION: 6

The line which makes intercepts 3 and 4 on the x and the y axis respectively, has equation

Solution:
Intercept form is

x/a +y/b =1

in this question

x/3 +y/4=1

by solving this equation, we get

4x + 3y =12

x/a +y/b =1

in this question

x/3 +y/4=1

by solving this equation, we get

4x + 3y =12

QUESTION: 7

Find the equation of line passing through the mid-point of line joining the points (3, 4) and (5, 6) and perpendicular to the equation of line 2x + 3y = 5.

Solution:

Mid Point [(3+5)/2, (4+6)/2]

= [8/2, 10/2]

= (4,5)

Perpendicular to the equation : 2x + 3y - 5 = 10

3x - 2y + k = 0

3(4) - 2(5) + k = 0

12 - 10 + k 0

k = -2

Therefore the equation is : 3x - 2y - 2 = 0

QUESTION: 8

A line is known with its slope and an intercept on one of the axes, then the equation of the line is in the form of:

Solution:

The slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the value of y at the y-intercept, which can be written as (0, b).

QUESTION: 9

For the line x+y = 1, what is the angle made with the positive direction of the x axis?

Solution:

We have in Equation = mx+c the slope of line as m and m=tanθ, θ is the angle made by (+ve) in X-axis

Hence, y = 1 - x

Here m = -1 = tanθ

θ = 135o

QUESTION: 10

The equation of the line through (a, b) with slope 1/2 is:

Solution:

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