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The number of points on the line 3x +4y ...

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

A

1

B

2

C

3

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
B
The perpendicular distance of (1,3) from the line `3x +4y =5` is 2 units while
`sec^(2) theta +2 cosec^(2) theta`
`= 3 +(tan theta -sqrt(2) cot theta)^(2) +2sqrt(2)`
`ge 3 +2 sqrt(2)`.
Evidently, there will be two such points on the line.
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