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  • Let be a straight line passing through the origin and <img alt="L 2" src="https://entrancecorner.oncodecogs.com/gif.lat

Let L 1 be a straight line passing through the origin and L 2 be the straight line  \mathrm{X+Y=1}. If the intercepts made by the circle \mathrm{x 2+y 2-x+3 y=0} on L1 and L2 are equal, then which of the following equations can represent L1 :

Option: 1

\mathrm{x+y=0}


Option: 2

\mathrm{x+y=0}


Option: 3

\mathrm{x+7 y=0}


Option: 4

\mathrm{ x-7 y=0}


Answers (1)

best_answer

Given \mathrm{P P^{\prime}=Q Q^{\prime} \Rightarrow\left(P P^{\prime}\right)^{2}=\left(Q Q^{\prime}\right)^{2}}

\mathrm{\Rightarrow \quad\left\{\left(O P^{\prime}\right)^{2}-(\mathrm{op})^{2}\right\}=\left(O Q^{\prime}\right)^{2}-(\mathrm{OQ})^{2}}
\mathrm{\Rightarrow \quad \mathrm{OP}=\mathrm{OQ}}



\mathrm{\quad\left|\frac{\frac{1}{2}-\frac{3}{2}-1}{\sqrt{2}}\right|=\left|\frac{\frac{m}{2}+\frac{3}{2}}{\sqrt{1+m^2}}\right|}
\mathrm{\Rightarrow \quad m=1,-1 / 7}
\mathrm{\Rightarrow \quad \text { lies are } y=x, y=-\frac{x}{7}}
Hence (C) is the correct answer.


 

Posted by

Nehul

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