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  • A variable line drawn through the point (1, 3) meets the x-axis at A and y-axis at B. If the rectangle OAPB is completed, where ‘O’ is the origin, then locus of ‘P’ is<d

A variable line drawn through the point (1, 3) meets the x-axis at A and y-axis at B. If the rectangle OAPB is completed, where ‘O’ is the origin, then locus of ‘P’ is

Option: 1

\frac{1}{y}+\frac{3}{x}=1


Option: 2

x+3 y=1


Option: 3

\frac{1}{x}+\frac{3}{y}=1


Option: 4

3 x+y=1


Answers (1)

best_answer

Let the line be \mathrm{\frac{x}{a}+\frac{y}{b}=1}. Since the line is passing through \mathrm{(1,3)}, hence \mathrm{\frac{1}{a}+\frac{3}{b}=1}.

Now \mathrm{A=(a, 0), B=(0, b) \Rightarrow P=(a, b)}

Thus locus of 'p' is \mathrm{\frac{1}{x}+\frac{3}{y}=1}


 

 

Posted by

Divya Prakash Singh

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