Question

Find the equation of the lines passing through the point (3,-2) and inclined at an angle of 60°  to line √3x+y=1

Answer 1

as you can see the fig
you have m1 = -√3 and slope of second line = m2 and TAN©=60°
apply the following formula
tan©=|m1-m2|÷|1+m1m2| (| | = modules)
you will get m2= -1/4 , √3
(rejected)
therefore you get m2 =√3
and you have two points on the line (3,-2)
apply point-slope form
you will get your answer

Answer 2

Answer:

y = √3x (or) y = 0

Step-by-step explanation:

ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴛʜᴇ ʟɪɴᴇ ᴘᴀꜱꜱᴇꜱ ᴛʜʀᴏᴜɢʜ ᴛʜᴇ ᴏʀɪɢɪɴ. ꜱᴏ, ɪᴛꜱ ᴄᴏᴏʀᴅɪɴᴀᴛᴇꜱ ᴡɪʟʟ ʙᴇ ᴏ(0,0)

ꜱʟᴏᴘᴇ ᴏꜰ ᴛʜᴇ ɢɪᴠᴇɴ ʟɪɴᴇ: √3x + ʏ = 1 ɪ.ᴇ ᴍ₁ = -√3.

ʟᴇᴛ ᴛʜᴇ ꜱʟᴏᴘᴇ ᴏꜰ ᴛʜᴇ ʀᴇQᴜɪʀᴇᴅ ʟɪɴᴇ ᴡʜɪᴄʜ ᴍᴀᴋᴇꜱ 60° ᴡɪᴛʜ ᴀʙᴏᴠᴇ ʟɪɴᴇ ɪꜱ ᴍ.

∴ ᴛᴀɴ 60° = |-√3 - ᴍ/1 - √3ᴍ|

⇒ √3 = |-√3 - ᴍ/1 - √3ᴍ|

⇒ -√3 - ᴍ = √3 - 3ᴍ (ᴏʀ) -√3 - ᴍ = -√3 + 3ᴍ

⇒ ᴍ = √3 (ᴏʀ) ᴍ = 0

ɢɪᴠᴇɴ ᴛʜᴀᴛ ʟɪɴᴇ ɪꜱ ᴘᴀꜱꜱɪɴɢ ᴛʜʀᴏᴜɢʜ (0,0).

ʜᴇɴᴄᴇ, ᴛʜᴇ ᴇQᴜᴀᴛɪᴏɴ ꜰᴏʀ ᴛʜᴇ ʀᴇQᴜɪʀᴇᴅ ʟɪɴᴇ ɪꜱ:

⇒ ʏ + 0 = √3(x - 0)  (ᴏʀ) ʏ + 0 = 0(x - 0)

⇒ ʏ = √3x       (ᴏʀ)  ʏ = 0

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘꜱ!