Question

If $x_1,x_2,x_3$ as well as $y_1,y_2,y_3$ are in G.P. with same common ratio, then the points $P\left(x_1,y_1\right)$, $Q\left(x_2,y_2\right)$ and $R\left(x_3,y_3\right)$

• A. lie on a straight line
• B. lie on an ellipse
• C. lie on a circle
• D. are vertices of a triangle

Answer 1

The correct option is A lie on a straight line

since they are in GP of the same ratio

$\frac{x_1}{y_1}=\frac{x_2}{y_2}=\frac{x_3}{y_3}⟹\frac{x}{y}=k$

$x=ky⟹x-ky=0$

It represents a straight line