THE STRIGHT LINE CUTS OFF INTERCEPTS FROM THE COORDINTE AXES ,THE SUM OF RECIPROCALS OF WHICH IS CONSTANT SHOW - Maths - Straight Lines

Question

THE STRIGHT LINE CUTS OFF INTERCEPTS FROM THE COORDINTE AXES ,THE
SUM OF RECIPROCALS OF WHICH IS CONSTANT SHOW THAT IT ALEAYS PASSES
THRUA FIXED POINT

Rajat Sethi · Accepted Answer

Let the equation of line be xa+yb=1
(i)i,e, Its intercepts on the axes are a and b respectively
Now,According to question,1a+1b=constant=1p(say)⇒1a+1b=1p⇒pa+pb=1
(ii)From (ii),it follows that the line (i) passes through the fixed point (p,p)

THE STRIGHT LINE CUTS OFF INTERCEPTS FROM THE COORDINTE AXES ,THE SUM OF RECIPROCALS OF WHICH IS CONSTANT .SHOW THAT IT ALEAYS PASSES THRUA FIXED POINT