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Standard XII

Mathematics

Polar Representation of a Complex Number

Let the given...

Question

Let the given line intersect x-axis at R. If a line through R intersects the hyperbola at S and T, then the minimum value of (RS) (RT) is ________

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4 √2

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Solution

The correct option is C
8

Locus of circum centre is rectangular hyperbola.

R = (2, 0) Any point through R is (2 + r cos $θ$ , r sin $θ$ )

$\Rightarrow$ (2 + r cos $θ$ ) (r sin $θ$ ) = 4

$\Rightarrow$ $r^{2}$ sin $θ$ cos $θ$ + 2 r sin $θ$ = 4

$∴ r_{1} r_{2}$ $= ∣ ∣ \frac{4}{s i n θ c o s θ} ∣ ∣ \geq 8$

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Let the given line intersect x-axis at R. If a line through R intersects the hyperbola at S and T, then the minimum value of (RS) (RT) is ________

The correct option is C 8 Locus of circum centre is rectangular hyperbola. R = (2, 0) Any point through R is (2 + r cosθ, r sin θ) ⇒ (2 + r cos θ ) (r sin θ ) = 4 ⇒ r2 sin θ cos θ + 2 r sin θ = 4 ∴r1r2 =∣∣4sinθcosθ∣∣≥8