Progression (Sequence and Series)Hard
Question
If x1, x2, x3 as well as y1, y2, y3 are in GP with the same common ratio, then the points (x1, y1), (x2, y2) and (x3, y3)
Options
A.lie on a straght line
B.lie on an ellipse
C.lie on a circle
D.are vertice of a triangle
Solution
Let 
and 
⇒ x2 = x1r, x3 = x1r3 y2 = y1r and y3 = y1r2
Again, ᐃ =
Applying R2 → R2 - rR1 and R3 → R3 - rR2
(∵ R2 and R3 are identical)
Hence, (x1, y1), (x2, y2), (x3, y3) lie on a straight line.
and ⇒ x2 = x1r, x3 = x1r3 y2 = y1r and y3 = y1r2
Again, ᐃ =
Applying R2 → R2 - rR1 and R3 → R3 - rR2
(∵ R2 and R3 are identical)Hence, (x1, y1), (x2, y2), (x3, y3) lie on a straight line.
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