The line x cos-y sin-p touches the hyperbola x2-a2-y2-b2-1- if

The correct option is C The equation of line is x cosα +y sinα =p ⇒ y = x cot α + p cosec α Now, c^2 = a^2m^2 b^2 ⇒ p^2 cosec α = a^2 cot^2 ...

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Byju's Answer

Standard XII

Mathematics

Parametric Form of Tangent: Hyperbola

The line x co...

Question

The line $x c o s α + y s i n α = p$ touches the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ , if

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Solution

The correct option is A

The equation of line is $x c o s α + y s i n α = p$
$\Rightarrow y = - x c o t α + p c o s e c α$
Now, $c^{2} = a^{2} m^{2} - b^{2}$
$\Rightarrow$ $p^{2} c o s e c α = a^{2} c o t^{2} α - b^{2}$
$\Rightarrow$ $a^{2} c o s^{2} α - b^{2} s i n^{2} α = p^{2}$

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Similar questions

The line $x cos α + y sin α = p$ touches the hyperbola
$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ if

Q. If the straight line

x cos α + y sin α = p

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a^{2} {cos}^{2} α + b^{2} {sin}^{2} α = p^{2}

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x cos α + y sin α = p

touches the curve

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

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a^{2} {cos}^{2} α - b^{2} {sin}^{2} α = p^{2}

If the straight line x cos $α$ + y sin $α$ = p touches the curve $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,$ then prove that $a^{2} c o s^{2} α + b^{2} s i n^{2} α = p^{2}$ .

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The line x cosα+y sin α=p touches the hyperbola x2a2−y2b2=1, if

The correct option is A The equation of line is x cosα+y sinα=p ⇒y=−x cot α+p cosec α Now, c2=a2m2−b2 ⇒ p2cosec α=a2cot2 α−b2 ⇒ a2cos2α−b2sin2α=p2

The line $x c o s α + y s i n α = p$ touches the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ , if

The correct option is A

The equation of line is $x c o s α + y s i n α = p$
$\Rightarrow y = - x c o t α + p c o s e c α$
Now, $c^{2} = a^{2} m^{2} - b^{2}$
$\Rightarrow$ $p^{2} c o s e c α = a^{2} c o t^{2} α - b^{2}$
$\Rightarrow$ $a^{2} c o s^{2} α - b^{2} s i n^{2} α = p^{2}$