The condition that the line x cos- y sin- p to be a tangent to the hyperbola x 2- a 2- y 2- b 2-1 isA- a2cos 2-b2sin 2-p2B- a2cos 2-b2sin 2-p2C- a2sin 2-b2cos 2-p2D- a2sin 2-b2cos 2-p2

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Integration Using Substitution

The condition...

Question

The condition that the line $x c o s α + y s i n α = p$ to be a tangent to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is

a^{2} c o s^{2} α + b^{2} s i n^{2} α = p^{2}

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a^{2} c o s^{2} α - b^{2} s i n^{2} α = p^{2}

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a^{2} s i n^{2} α + b^{2} c o s^{2} α = p^{2}

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a^{2} s i n^{2} α + b^{2} c o s^{2} α = p^{2}

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Solution

The correct option is B $a^{2} c o s^{2} α - b^{2} s i n^{2} α = p^{2}$

$l = c o s α, m = s i n α, n = - p$
$a^{2} l^{2} - b^{2} m^{2} = n^{2} \Rightarrow p^{2} = a^{2} c o s^{2} α - b^{2} s i n^{2} α$

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Similar questions

Q. If the line

x cos α + y sin α = p

is a tangent to the ellipse

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

then prove that

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

Q. 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} {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 $a^{2} c o s^{2} α + b^{2} s i n^{2} α = p^{2}$ .

Q. 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} {cos}^{2} α - b^{2} {sin}^{2} α = p^{2}

Q. If the straight line xcos

α

+ ysin

α

= p touches the curve

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

, then prove that a²cos²

α

-

b²sin²

α

= p².

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The condition that the line x cos α+y sin α=p to be a tangent to the hyperbola x2a2−y2b2=1 is

The correct option is B a2cos2α−b2sin2α=p2 l=cos α,m = sin α, n=−p a2l2−b2m2=n2⇒p2=a2 cos2α−b2 sin2α

The condition that the line $x c o s α + y s i n α = p$ to be a tangent to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ is

The correct option is B $a^{2} c o s^{2} α - b^{2} s i n^{2} α = p^{2}$

$l = c o s α, m = s i n α, n = - p$
$a^{2} l^{2} - b^{2} m^{2} = n^{2} \Rightarrow p^{2} = a^{2} c o s^{2} α - b^{2} s i n^{2} α$