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

Options

A. 1
B. 2
C. 3
D. infinite

Answer

B

Explanation

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.