InterviewSolution
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InterviewSolution
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Show that the point `(x ,y)`given by `x=(2a t)/(1+t^2)a n dy=((1-t^2)/(1+t^2))`lies on a circle for all real values of `t`such that `-1lt=tlt=1,`where a is any given real number. |
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Answer» Given points are `x=(2at)/(1+t^(2))` and `y=(a(1-t^(2)))/(1+t^(2))` `because x^(2)+y^(2)=(4a^(2)t^(2))/((1+t^(2))^(2))+(a^(2)(1-t^(2)))/(1+t^(2))` `rArr1/(a^(2)(x^(2)+y^(2)))=(4t^(2)+1+t^(4)-2t^(2))/((1+t^(2))^(2))` `rArr1/(a^(2))(x^(2)+y^(2))=(t^(2)+2t^(2)+1)/((1+t^(2))^(2))` `rArr 1/(a^(2))(x^(2)+y^(2))=((1+t^(2))^(2))/((1+t^(2))^(2))` `rArr x^(2)+y^(2)=a^(2)`, which is a required circle. |
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