The given line is bx+ay=ab.
Foot of perpendicular from origin
bx=ay=−[a2+b2−ab]
x=a2+b2ab2,y=a2+b2a2b
x2+y2=(a2+b2)2a2b2(a2+b2)
x2+y2=a2+b2a2b2
given a21+b21=41
a2b2a2+b2=41
⇒x2+y2=4, which is equation of circle.
Let a and b be any two numbers satisfying a21+b21=41. Then, the foot of perpendicular from the origin on the variable line ax+by=1 lies on :
Held on 9 Apr 2014 · Verified 6 Jul 2026.
A circle of radius =2
A hyperbola with each semi-axis =2.
A hyperbola with each semi-axis =2
A circle of radius =2
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