A hyperbola is given as x2- 2-y2-cosec2-1What-s the eccentricty of the hyperbola-

The correct option is A Given hyperbola is, x^2/cos^2α y^2/sin^2α=1 Comparing this with standard hyperbola, a^2=cos^2α b^2=sin^2α e^2=1+b^2/a^2 =1+sin^2∝/cos^ ...

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Standard XII

Mathematics

Real Valued Functions

A hyperbola i...

Question

A hyperbola is given as $x^{2} . s e c^{2} α - y^{2} . c o s e c^{2} α = 1$

What's the eccentricty of the hyperbola?

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Solution

The correct option is A

Given hyperbola is,

$\frac{x^{2}}{c o s^{2} α} - \frac{y^{2}}{s i n^{2} α} = 1$

Comparing this with standard hyperbola,

$a^{2} = c o s^{2} α$

$b^{2} = s i n^{2} α$

$e^{2} = 1 + \frac{b^{2}}{a^{2}}$

$= 1 + \frac{s i n^{2} \propto}{c o s^{2} \propto} = 1 + t a n^{2} \propto$

$= s e c^{2} α$

$e = | s e c \propto |$ .

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Similar questions

Q. The distance between the foci of a hyperbola is 16 and its eccentricity is

\sqrt{2}

, then equation of the hyperbola is
(a) x² + y² = 32
(b) x² − y² = 16
(c) x² + y² = 16
(d) x² − y²= 32

The length of the transverse axis of a hyperbola is 2cos t. The foci of the hyperbola are the same as that of the ellipse $9 x^{2} + 16 y^{2} = 144$ .
The equation of the hyperbola is ___

What is the conjugate hyperbola of the hyperbola
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1. The particular kind of hyperbola in which the lengths of the transverse and conjugate axis are equal is called an equilateral hyperbola.

2. Eccentricity of equilateral hyperbola = $\sqrt{2}$
3. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = 0$

4. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = - a^{2}$

Q. The angle between asymptotes of the standard hyperbola (centered at origin and

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A hyperbola is given as x2.sec2α−y2.cosec2α=1 What's the eccentricty of the hyperbola?

The correct option is A Given hyperbola is, x2cos2α−y2sin2α=1 Comparing this with standard hyperbola, a2=cos2α b2=sin2α e2=1+b2a2 =1+sin2∝cos2∝=1+tan2 ∝ =sec2α e=|sec∝|.

A hyperbola is given as $x^{2} . s e c^{2} α - y^{2} . c o s e c^{2} α = 1$

What's the eccentricty of the hyperbola?