Question

find the equations of the lines passing through the point (3,-2) and inclined at an angle of 60° to the line root3x + y =1?

Answer 1

3X+4y=1. 3(3)+4(-2) =1 9-8=1 1=1

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!