Question

If x₁, x₂, x₃ and y₁, y₂, y₃ are both in GP with the same common ratio, then the points (x₁, y₁), (x₂, y₂) and (x₃, y₃)

(a) lie on a straight line

(b) lie on an ellipse

(c) lie on a circle

(d) are veitices of a triangle

Answer 1

Correct Option (a) lie on a straight line

Explanation:

Since, x₁, x₂, x₃ and y₁, y₃ are in GP

Then, x₂ = rx₁,  x₃ = r²x₁ 

and    y₂ = ry₁,  y₃ = r²y₁, 

where, r is a common ratio.

The points become (x₁, y₁), (r x₁, r y₁) and (r²x₁, r²y₁)