Hyperbola - Maharashtra Board STD 11 Maths Questions

Q 1MCQ1 Mark

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

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

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

Answer: D.

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Q 6Solve the following 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 7Solve the following 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 8Solve the following 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 9Solve the following 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 10Solve the following 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 11Solve the Following Question.(4 Marks)4 Marks

Find the equation of the hyperbola whose
Vertices are (-8, -1) and (-4, 4) and focus is (17, -1)

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Q 12Solve the Following Question.(4 Marks)4 Marks

If P is any point on the hyperbola whose axis are equal, prove that SP . SP =$\text{CP}^{2}$

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Q 13Solve the Following Question.(4 Marks)4 Marks

Find the equation of the hyperbola whoseFoci are (6, 4) and (-4, 4) and eccentricity is 2.

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Q 14Solve the Following Question.(4 Marks)4 Marks

Find the center, eccentricity, foci and directrices of the hyperbola
$\text{x}^{2}-3\text{y}^{2}-2\text{x}=8.$

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Q 15Solve the Following Question.(4 Marks)4 Marks

Find the eccentricity of the hyperbola, the length of whose conjugate axis is $\frac{3}{4}$ of the length of transvers axis.

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Q 16Solve the Following Question.(5 Marks)5 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 17Solve the Following Question.(5 Marks)5 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 18Solve the Following Question.(5 Marks)5 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 19Solve the Following Question.(5 Marks)5 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 20Solve the Following Question.(5 Marks)5 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

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