Test: Various Forms Of Equation Of A Line - JEE MCQ

This question can be done by picking the options.
a₁/a₂ = b₁/b₂ = c₁/c₂
Equation : 2x + y = 3
(d) 4x + 2y = 6
a₁ = 2⇒, b₁ = 1, c₁ = 3
a₂ = 4, b₂ = 2, c₂ = 6
⇒ 2/4 = 1/2 = 3/6
=> 1/2 = 1/2 = 1/2

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 
xcos60° + ysin60° = 2a
x(1/2) + y(√3/2) = 2a
x + √3y = 4a

The correct option is A

x/4+y/3=1

The equation of a line in the intercept form where the x intercept is a and y intercept is

b, is given by x/a+y/b=1.

So, substituting a=4 and b=3 we get the answer.

Consider the given points. (a²,0) and (0,b²)
We know that the equation of the line which is passing through the points
y−y₁ =[ (y₂−y₁) / (x₂−x₁)] (x−x₁)
So, y−0 = b²−0/0-a²(x-a²)
-ya² - b²x = -b²a²
xb² +ya² = b²a²

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

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

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).

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