Question

please answer this question ​

Answer 1

Qᴜᴇsᴛɪᴏɴ :-

The equation of a line parallel to x - axis and at a distance of 6 units from origin is ?

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

• The equation of a straight line parallel to x - axis at a distance b from it is y = a.

• The equation of x - axis is y = 0, since, x - axis is a parallel to itself at a distance 0 from it.

Here we have to case :-

• if the straight line is parallel to x - axis and b units above the x - axis , we have , equation of line , y = a .
• if the straight line is parallel to x-axis and b units below the x - axis , we have , equation of line , y = (-a) .

where "a" denotes the distance from origin..

Sᴏʟᴜᴛɪᴏɴ :-

here we have given that,

→ Distance from origin = 6 units . = a

So,

→ Equation of line parallel to x axis :- y = a

→ a = 6 units.

Therefore,

→ The equation will be y = 6. (Ans.)

Hence ,the line y - 6 = 0 is the line parallel to x axis and at a distance of 6 units from the origin..

{ Note :- in Question it is not clearly written if the line is above x-axis , or below, so i assumed above. Remember that, sign will change if it is below the x - axis. }