Hyperbola - Gujarat Board (GSEB) STD 11 Science MATHS Questions

Q 1MCQ1 Mark

Equation of the hyperbola whose vertices are $( \pm 3,0)$ and foci at $( \pm 5,0)$, is

✓
$16 x^2-9 y^2=144$
B
$9 x^2-16 y^2=144$
C
$25 \mathrm{x}^2-9 \mathrm{y}^2=225$
D
$9 x^2-25 y^2=81$

Answer: A.

Q 2MCQ1 Mark

If $e_1$ and $e_2$ 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 $e_1$ and $e_2$ is

A
$3\text{e}_1^2 + \text{e}_2^2 = 2$
B
$\text{e}_1^2 + 2\text{e}_2^2 = 3$
✓
$2\text{e}_1^2 +\text{e}_2^2 = 3$
D
$\text{e}_1^2 + 3\text{e}_2^2 = 2$

Answer: C.

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Q 3MCQ1 Mark

The eccentricity of the hyperbola $x^2 - 4y^2 = 1$

A
$\frac{\sqrt3}{2}$
✓
${\frac{\sqrt5}{2}}$
C
${\frac{2}{\sqrt3}}$
D
$\frac{2}{\sqrt5}$

Answer: B.

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Q 4MCQ1 Mark

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

✓
$8\sqrt2$
B
$16\sqrt2$
C
$4\sqrt2$
D
$6\sqrt2$

Answer: A.

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Q 5MCQ1 Mark

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

A
$x y=1$
B
$2 x y+4 x-4 y-1=0$
C
$x^2-y^2=1$
✓
$2 x y-4 x+4 y+1=0$

Answer: D.

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Q 6(Each question 1 marks)1 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 7(Each question 1 marks)1 Mark

Write the lenght of the latus-rectum of the hyperbola $16\text{x}^{2}-9\text{y}^{2}=144$

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Q 8(Each question 1 marks)1 Mark

Wrie the eccentricity of the hyperbola whose latus-rectum is half of its transversw axis.

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Q 9(Each question 1 marks)1 Mark

If the latus-rectum throught one focus of a hyperbola subtends a right angle at the farther vertex, then write the eccentricity of the hyperbola.

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Q 10(Each question 1 marks)1 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 11(Each question 4 marks)4 Marks

Find the equation of the hyperbola whose vertices are at $(\pm6, 0)$ and one of the directrices is x = 4

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Q 12(Each question 4 marks)4 Marks

In each the following find the equation of the hyperbola satisfying the given conditions: Foci $(0, \pm13), $ conjugate axis = 24

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Q 13(Each question 4 marks)4 Marks

Find the equation of the hyperbola whose,Focus is (2, 2) directrix is $\text{x+y}=\text{9}$ and eccentricity = 2

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Q 14(Each question 4 marks)4 Marks

Find the eccentricity, coordinates of the foci, equation of the directrices and lenght of the latus-rectum of the hyperbola $9\text{x}^{2}-16\text{y}^{2}=144$

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Q 15(Each question 4 marks)4 Marks

Find the equation of the hyperbola whoseFocus is at $(5, 2)$, vertex at $(4, 2)$ and center at $(3, 2)$

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Hyperbola MATHS - Hyperbola

Hyperbola question types

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