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# A straight line makes an intercept on the y-axis twice as long as that on the x-axis and is at a unit distance from the origin. Determine its equation.

siddharth gupta
28 Points
7 years ago
intercept form:
x/a+y/2a=1
on solving 2x+y=2a.......(1.)
normal form:
xcos(m)+ysin(m)=1.........(2.)
now adjust eqn (1.) to obtain eqn(2)
i.e make the sum of squares of coefficients of x and y in eq.(1) equal to 1
for that divide the eqn. on both sides by ((2)2+(1)2)1/2
the resultant eqn. is (2/(5)1/2)x+(1/(5)1/2)y=2/(5)1/2a.....(3.)
on comparing with eqn(2) a=(5)1/2/2
put the value of a in eqn 2
RESULT IS:2x+y=(5)1/2
WITH REGARDS
SIDDHARTH GUPTA
no
Arun Kumar IIT Delhi
7 years ago
Hello
$\\y=mx+c \\=>y_{interc}=c \\=>x_{interc}=-c/m \\=>m=-1 \\distance={c \over \sqrt{1+m^2}} \\={c \over \sqrt{2}}=\pm 1 \\=>c=\pm \sqrt{2}$
Thanks & Regards
Arun Kumar
Btech, IIT Delhi