JEE Main & Advanced Mathematics Straight Line Question Bank Critical Thinking

  • question_answer If \[{{x}_{1}},{{x}_{2}},{{x}_{3}},\,\,\text{and }\,{{y}_{1}},{{y}_{2}},{{y}_{3}}\] are both in G.P. with the same common ratio, then the points \[({{x}_{1}},{{y}_{1}}),\] \[({{x}_{2}},\,{{y}_{2}})\] and \[({{x}_{3}},\,{{y}_{3}})\][AIEEE 2003]

    A)            Lie on a straight line                 

    B)            Lie on an ellipse

    C)            Lie on a circle                            

    D)            Are vertices of a triangle

    Correct Answer: A

    Solution :

               Taking co-ordinates as \[\left( \frac{x}{r},\,\frac{y}{r} \right)\]; \[(x,\,y)\,\text{and}\,(xr,\,yr)\]                    Above co-ordinates satisfy the relation \[y=mx\], so lie on a straight line.

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