JEE Mains · Maths · STD 11 - 9. straight line
Let two straight lines drawn from the origin \(O\) intersect the line \(3 x+4 y=12\) at the points \(P\) and \(\mathrm{Q}\) such that \(\triangle \mathrm{OPQ}\) is an isosceles triangle and \(\angle \mathrm{POQ}=90^{\circ}\). If \(l=\mathrm{OP}^2+\mathrm{PQ}^2+\mathrm{QO}^2\), then the greatest integer less than or equal to \(l\) is :
- A \(44\)
- B \(48\)
- C \(46\)
- D \(42\)
Answer & Solution
Correct Answer
(C) \(46\)
Step-by-step Solution
Detailed explanation
\( 3 \mathrm{x}+4 \mathrm{y}=12 \) \( 3(\mathrm{r} \cos \theta)+4(\mathrm{r} \sin \theta)=12 \) \( \mathrm{r}(3 \cos \theta+4 \sin \theta)=12 \ldots(1) \) \( 3(-\mathrm{r} \sin \theta)+4(\mathrm{r} \cos \theta)=12 \) \( \mathrm{r}(-3 \sin \theta+4 \cos \theta)=12 \ldots(2) \)…
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