The equation of one of the straight lines which passes through the point ( 1 , 3 ) and makes an angles tan -…

The equation of one of the straight lines which passes through the point (1,3) and makes an angles tan-1(2) with the straight line, y+1=32x is
  1. 42x+5y-(15+42)=0
  2. 52x+4y-(15+42)=0
  3. 42x+5y-42=0
  4. 42x-5y-(5+42)=0

Solution

y=mx+c

3=m+c

2=m-321+32m

⇒6m+2=±m-32

from Positive sign

⇒5m=-42 ⇒m=-425

from negative sign

⇒6m+2=-m+32

⇒7 m=22⇒m=227

According to options take m=-425

So y=-42x5+3+425

42x+5y-(15+42)=0

Asked in: JEE Main 2021 (18 Mar Shift 1)

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