The number of points on the line 3 x-4 y-5- which are at a distance of 2-2 cosec2- - R- form the point 1-3- is

The perpendicular distance of (1, 3) from the line 3x + 4y = 5 is 2 units while, sec^2θ + 2 cosec^2θ≥ 3 as sec^2θ, cosec^2θ≥ 1 Evidently, these will be two suc ...

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Standard XII

Mathematics

Secant of a Curve y =f(x)

The number of...

Question

The number of points on the line 3x + 4y = 5, which are at a distance of $s e c^{2} θ + 2 c o s e c^{2} θ, θ ϵ R,$ form the point (1,3), is

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Solution

The perpendicular distance of (1, 3) from the line 3x + 4y = 5 is 2 units while,
$s e c^{2} θ + 2 c o s e c^{2} θ \geq 3$ {as $s e c^{2} θ, c o s e c^{2} θ \geq 1$ }
Evidently, these will be two such points on the line.

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The number of points on the line 3x + 4y = 5, which are at a distance of sec2θ+2cosec2θ, θϵR, form the point (1,3), is

The perpendicular distance of (1, 3) from the line 3x + 4y = 5 is 2 units while, sec2θ+2cosec2θ≥3 {as sec2θ, cosec2θ≥1} Evidently, these will be two such points on the line.

The number of points on the line 3x + 4y = 5, which are at a distance of $s e c^{2} θ + 2 c o s e c^{2} θ, θ ϵ R,$ form the point (1,3), is

The perpendicular distance of (1, 3) from the line 3x + 4y = 5 is 2 units while,
$s e c^{2} θ + 2 c o s e c^{2} θ \geq 3$ {as $s e c^{2} θ, c o s e c^{2} θ \geq 1$ }
Evidently, these will be two such points on the line.