Hyperbola - Rajasthan Board (RBSE) STD 11 Science MATHS Questions

Equation of the hyperbola whose vertices are $(\pm3,0)$ and foci at $(\pm5,0),$ is

16x² - 9y² = 144
9x² - 16y² = 144
25x² - 9y² = 225
9x² - 25y² = 81

If e₁ and e₂ are respectively the eccentricities of the ellipse $\frac{\text{x}^2}{18}+\frac{\text{y}^2}{4}=1$ and the hyperbola $\frac{\text{x}^2}{9}-\frac{\text{y}^2}{4}=1,$ then the relation between e₁ and e₂ is

$3\text{e}_1^2 + \text{e}_2^2 = 2$
$\text{e}_1^2 + 2\text{e}_2^2 = 3$
$2\text{e}_1^2 +\text{e}_2^2 = 3$
$\text{e}_1^2 + 3\text{e}_2^2 = 2$

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Q 3M.C.Q (1 Marks)1 Mark

The eccentricity of the hyperbola x² - 4y² = 1

$\frac{\sqrt3}{2}$
${\frac{\sqrt5}{2}}$
${\frac{2}{\sqrt3}}$
$\frac{2}{\sqrt5}$

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Q 4M.C.Q (1 Marks)1 Mark

The distance between the directrices of the hyperbola $\text{x}=8\sec\theta,\text{y}=8,$ is

$8\sqrt2$
$16\sqrt2$
$4\sqrt2$
$6\sqrt2$

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Q 5M.C.Q (1 Marks)1 Mark

The equation of the conic with focus at (1, -1) directrix along x - y + 1 = 0 and eccentricity $\sqrt2$ is

xy = 1
2xy + 4x - 4y - 1 = 0
x² - y² = 1
2xy - 4x + 4y + 1 = 0

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Q 61 Marks Question1 Mark

If the foci of the ellipse $\frac{\text{x}^{2}}{16}+\frac{\text{y}^{2}}{\text{b}^{2}}=1$ and the hyperbola $\frac{\text{x}^{2}}{144}-\frac{\text{y}^{2}}{81}=\frac{1}{25}$ coincide, value of $\text{b}^{2}$

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Q 71 Marks Question1 Mark

Wrie the coordinates of the foci of the hyperbola $9\text{x}^{2}-16\text{y}^{2}=144$

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Q 81 Marks Question1 Mark

If e and e are respectively the eccentricities of the ellipse $\frac{\text{x}^2}{18}+\frac{\text{y}^2}{4}=1$ and the hyperbola $\frac{\text{x}^2}{9}-\frac{\text{y}^2}{4}=1,$ then write the value of $2\text{e}_1^2 +\text{e}_2^2.$

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Q 91 Marks Question1 Mark

Write the distance between the directrices of the hyperbola $\text{x}=8\sec\theta,\ \text{y}=8\tan\theta.$

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Q 101 Marks Question1 Mark

Write the equation of the hyperbola whose vertices are $(\pm3,0)$ and foci at $(\pm5,0).$

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Q 115 Marks Questions5 Marks

Find the eccentricity, coordinates of the foci, equations of directrices and lenght of the latus-rectum of the hyperbola
$2\text{x}^{2}-3\text{y}^{2}=5.$

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Q 125 Marks Questions5 Marks

Find the equation of the hyperbola whose

Foci at $(\pm2, 0)$ and eccentricity is $\frac{3}{2}$. [NCRT EXEMPLAR]

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Q 135 Marks Questions5 Marks

Find the equation of the hyperbola whose

Foci are (6, 4) and (-4, 4) and eccentricity is 2.

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Q 145 Marks Questions5 Marks

Find the equation of the hyperbola whose

Vertices are at $(0 \pm 7)$ and foci at $\big(0, + \frac{28}{3}\big).$