If $\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3$ and $\mathrm{y}_1, \mathrm{y}_2, \mathrm{y}_3$ are both in G.P…
If $\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3$ and $\mathrm{y}_1, \mathrm{y}_2, \mathrm{y}_3$ are both in G.P. with the same common ratio, then the points $\left(\mathrm{x}_1, \mathrm{y}_1\right),\left(\mathrm{x}_2, \mathrm{y}_2\right)$ and $\left(\mathrm{x}_3\right.$, $\mathrm{y}_3$ )
are vertices of a triangle
lie on a straight line
lie on an ellipse
lie on a circle
Solution
Taking co-ordinates as $\left(\frac{\mathrm{x}}{\mathrm{r}}, \frac{\mathrm{y}}{\mathrm{r}}\right) ;(\mathrm{x}, \mathrm{y}) \&(\mathrm{xr}, \mathrm{yr})$. Above coordinates satisfy the relation $\mathrm{y}=\mathrm{mx}$ Therefore lies on the straight line.