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The number of points on the line \mathrm{3 x+4 y=5}, which are at a distance of \mathrm{\sec ^{2} \theta+2\operatorname{cosec}^{2} \theta, \theta \in R}, from the point \mathrm{(1,3)}, is

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

infinite


Answers (1)

best_answer

The distance of the point (1,3) from the line \mathrm{3 x+4 y=5} is \mathrm{2 / 5}. Now the value of \mathrm{\sec ^{2} \theta+2 \operatorname{cosec} e^{2} \theta} is greater than \mathrm{2 / 5}. hence two such lines will be possible. 

Hence (B) is the correct answer.

Posted by

shivangi.shekhar

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