Straight Line Question 221

Question: A line which makes an acute angle $ \theta $ with the positive direction of x-axis is drawn through the point P(3, 4) to meet the line $ x=6 $ at R and $ y=8 $ at S, then

Options:

A) $ PR=3\cos \theta $

B) $ PS=-4\cos ec\theta $

C) $ PR-PS=\frac{2(3sin\theta +4cos\theta )}{\sin 2\theta } $

D) $ \frac{9}{{{(PR)}^{2}}}+\frac{16}{{{(PS)}^{2}}}=1 $

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Answer:

Correct Answer: D

Solution:

  • [d] The equation of the line in parametric form is $ \frac{x-3}{\cos \theta }=\frac{y-4}{\sin \theta }=r $ Any point on this line is $ (3+rcos\theta ,4+rsin\theta ) $ It lies on $ x=6 $ if $ 3+r\cos \theta =6\Rightarrow r=3\sec \theta $

$ \therefore PR=3sec\theta $ Again the point lies on $ y=8 $ if $ 4+r\sin \theta =8 $

$ \therefore r=4\cos ec\theta $ or $ PS=4\cos ec\theta $ other options can be chocked easily