JEEmetry...
Geometry
Level
4
Find the equation of straight line which passes through the point of intersection of lines 3x-4y+1=0 and 5x+y-1=0 , and cuts equal intercepts from the axes.
3x-8y+11=0 and 11x-23y=0
8x-3y=0 and 23x+23y-11=0
None of these
23x-3y=0 and 8x+11y=0
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1 solution
Let 3 x − 4 y + 1 + a ( 5 x + y − 1 ) be required line.
⇒ ( 3 + 5 a ) x + ( a − 4 ) y + 1 − a = 0
So, X-intercept= 3 + 5 a a − 1
and Y-intercept= a − 4 a − 1
As it cuts equal intercepts:
3 + 5 a a − 1 = a − 4 a − 1
⇒ a=1, 4 − 7
Putting values of a in required equation we get,
⇒ 8x-3y=0 and 23x+23y-11=0