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If $x_{1}, x_{2}, x_{3}$ and $y_{1}, y_{2}, y_{3}$ are both in G.P. with the same common ratio, then the points $(x_{1}, y_{1})$ $(x_{2}, y_{2}) and (x_{3}, y_{3})$

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detailed solution

Correct option is D

Let x2=x1r,x3=x1r2y2=y1r,y3=y1r2The given points lie on the linex1y−y1x=0 for all values of r.

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If x1,x2,x3 and y1,y2,y3 are both in G.P. with the same common ratio, then the points x1,y1 x2,y2 and x3,y3

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If $x_{1}, x_{2}, x_{3}$ and $y_{1}, y_{2}, y_{3}$ are both in G.P. with the same common ratio, then the points $(x_{1}, y_{1})$ $(x_{2}, y_{2}) and (x_{3}, y_{3})$