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  • Try this! - Consider the set of all lines such that . Which one of the following statements is true? - Co-ordinate geometry - JEE Main

Consider the set of all lines px + qy +r =0 such that 3p + 2q + 4r = 0 . Which one of the following statements is true?

  • Option 1)

    The lines concurrent at the point \left(\frac{3}{4}, \frac{1}{2} \right )

  • Option 2)

    Each line passes through the origin.

  • Option 3)

    The lines are all parallel

  • Option 4)

    The lines are not concurrent.

Answers (1)

best_answer

 

Intercept form of a straight line -

\frac{x}{a}+\frac{y}{b}=1

 

- wherein

a and b are the x-intercept and y -intercept respectively.

 

Set of all line is px+qy+r=0

and given that 3p+2q+4r=0......

\Rightarrow \frac{3}{4}p+\frac{2}{4}q+r=0

compare with set of all line equation

x=\frac{3}{4},\: \: \: \: \: \: \: \: y=\frac{1}{2}

Hence, All line pass through a fixed point 

\left ( \frac{3}{4},\frac{1}{2} \right )


Option 1)

The lines concurrent at the point \left(\frac{3}{4}, \frac{1}{2} \right )

Option 2)

Each line passes through the origin.

Option 3)

The lines are all parallel

Option 4)

The lines are not concurrent.

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