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What is locus of the point ( a(cosx +sinx),b(cosx-sinx))

What is locus of the point ( a(cosx +sinx),b(cosx-sinx))

Grade:6

1 Answers

nitish
36 Points
4 years ago
actually in these type of questions we need to eliminate the parametic terms
in this case we need to eliminate the cosx and sinx terms.
so, i can write 
X=a(cosx+sinx) => X/a=(cosx+sinx) ------->(1)
and Y/b=(cosx-sinx)--------->(2)
 
squaring and adding equations (1) and (2);
(X/a)^2+(Y/b)^2=2
hence it represents an ellipse.
 
i hope you understand.

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