21think graficaly, and u'll know that
at origin, their tangents are PERPENDICULAR to each other!!!!
Wat is the basic condition for two curves to be orthogonal ??
I know they need to intersect at 90° but wat abt the CASE WER the two CURVES INTERSECT EACH OTHER MORE THAN ONCE ???
eg. x2 = y and y2 = x
are these said to be orhtogonal ???
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33 Answers
11yup tapan u r right
the basic condition is that their tangents mumust be perp .
and @ sky x=0 and y=0 r perp
but where is m1m2=-1
21
1x2=y , y2=x
these intersect at 2 real points:
x4-x=0 => x(x3-1)=0
0 and 1
now slope of tangents at the two curves:
x2=y => dy/dx=2x ---------- #1
y2=x => dy/dx=1/2y ---------#2
now see tangent slopes at the points of intersections.
if they satisfy m1.m2=-1 then they are orthogonal.. else not..
here these curves are not orthogonal [error ... ].