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If (a,a^{2})   falls inside the angle made by the lines y=\frac{x}{2},x> 0\; and \, y=3x,x> 0,\; then\; a belongs to

  • Option 1)

    \left ( 0,\; \frac{1}{2} \right )\;

  • Option 2)

    \; (3,\infty )\;

  • Option 3)

    \; \left ( \frac{1}{2},\; 3 \right )\;

  • Option 4)

    \; \left ( -3,\; -\frac{1}{2} \right )\;

 

Answers (1)

best_answer

As we learnt in 

Slope of a line -

m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

- wherein

Slope of line joining A(x1,y1) and  B(x2,y2) .

Slope of OP=\frac{a^{2}}{a}=a

now  slop of  y=\frac{x}{2}  is   m=\frac{1}{2}

Slop of y=3x is m=3

Thus   \frac{1}{2}<a<3

 

 


Option 1)

\left ( 0,\; \frac{1}{2} \right )\;

Incorrect option

Option 2)

\; (3,\infty )\;

Incorrect option

Option 3)

\; \left ( \frac{1}{2},\; 3 \right )\;

Correct option

Option 4)

\; \left ( -3,\; -\frac{1}{2} \right )\;

Incorrect option

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Aadil

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