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Select the correct option from the given alternatives The eccentricity of rectangular hyperbola is - Mathematics and Statistics

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प्रश्न

Select the correct option from the given alternatives

The eccentricity of rectangular hyperbola is

पर्याय

  • `1/2`

  • `1/(2 1/2)`

  • `2 1/2`

  • `1/(3 1/2)`

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उत्तर

The eccentricity of rectangular hyperbola is `2 1/2`

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Conic Sections - Hyperbola
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 7: Conic Sections - Miscellaneous Exercise 7 [पृष्ठ १७७]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 7 Conic Sections
Miscellaneous Exercise 7 | Q I. (11) | पृष्ठ १७७

संबंधित प्रश्‍न

Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/25 - y^2/16` = 1


Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

`x^2/25 - y^2/16` = – 1


Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

16x2 – 9y2 = 144


Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:

21x2 – 4y2 = 84


Find the equation of the hyperbola with centre at the origin, length of conjugate axis 10 and one of the foci (–7, 0).


Find the eccentricity of the hyperbola, which is conjugate to the hyperbola x2 – 3y2 = 3


If e and e' are the eccentricities of a hyperbola and its conjugate hyperbola respectively, prove that `1/"e"^2 + 1/("e""'")^2` = 1


Find the equation of the hyperbola referred to its principal axes:

whose distance between directrices is `8/3` and eccentricity is `3/2`


Find the equation of the hyperbola referred to its principal axes:

whose length of conjugate axis = 12 and passing through (1, – 2)


Find the equation of the hyperbola referred to its principal axes:

which passes through the points (6, 9) and (3, 0)


Find the equation of the hyperbola referred to its principal axes:

whose length of transverse and conjugate axis are 6 and 9 respectively


Find the equation of the tangent to the hyperbola:

3x2 – y2 = 4 at the point `(2, 2sqrt(2))`


Find the equation of the tangent to the hyperbola:

3x2 – 4y2 = 12 at the point (4, 3)


Find the equation of the tangent to the hyperbola:

9x2 – 16y2 = 144 at the point L of latus rectum in the first quadrant


Find the equations of the tangents to the hyperbola `x^2/25 - y^2/9` = 1 making equal intercepts on the co-ordinate axes


Find the equations of the tangents to the hyperbola 5x2 – 4y2 = 20 which are parallel to the line 3x + 2y + 12 = 0


Select the correct option from the given alternatives:

If the line 2x − y = 4 touches the hyperbola 4x2 − 3y2 = 24, the point of contact is


Select the correct option from the given alternatives:

The foci of hyperbola 4x2 − 9y2 − 36 = 0 are


Answer the following:

Find the equation of the hyperbola in the standard form if Length of conjugate axis is 5 and distance between foci is 13.


Answer the following:

Find the equation of the hyperbola in the standard form if length of the conjugate axis is 3 and distance between the foci is 5.


Answer the following:

Find the equation of the tangent to the hyperbola 7x2 − 3y2 = 51 at (−3, −2)


Answer the following:

Find the equations of the tangents to the hyperbola 3x2 − y2 = 48 which are perpendicular to the line x + 2y − 7 = 0


Answer the following:

Two tangents to the hyperbola `x^2/"a"^2 - y^2/"b"^2` = 1 make angles θ1, θ2, with the transverse axis. Find the locus of their point of intersection if tan θ1 + tan θ2 = k


The eccentricity of the hyperbola 25x2 - 9y2 = 225 is ______.


Let H: `x^2/a^2 - y^2/b^2` = 1, a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is `4(2sqrt(2) + sqrt(14))`. If the eccentricity H is `sqrt(11)/2`, then the value of a2 + 2b2 is equal to ______.


A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola `x^2/4 - y^2/2` = 1 at the point (x1, y1). Then `x_1^2 + 5y_1^2` is equal to ______.


(x – 1)2 + (y – 2)2 = `(3(2x + 3y + 2)^2)/13`represents hyperbola whose eccentricity is ______.


Parametric form of the hyperbola `x^2/4 - y^2/9` = –1 is ______.


The number of points from where a pair of perpendicular tangents can be drawn to the hyperbola, x2sec2α – y2cosec2α = 1, `α∈(0, π/4)` are ______.


The hyperbola `x^2/a^2 - y^2/b^2` = 1 passes through the point of intersection of the lines, 7x + 13y – 87 = 0 and 5x – 8y + 7 = 0, the latus rectum is `32sqrt(2)/5`. The value of `(asqrt(2) + b)` will be ______.


If the radii of director circles of `x^2/a^2 + y^2/b^2` = 1 and `x^2/a^2 - y^2/b^2` = (a > b) are 2r and r respectively, then `e_2^2/e_1^2` is equal to ______.

(where e1, e2 are their eccentricities respectively)


Let the hyperbola H : `x^2/a^2 - y^2/b^2` = 1 pass `(2sqrt(2), -2sqrt(2))`. A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola?


For the Hyperbola `x^2/(cos^2α) - y^2/(sin^2α)` = 1, which of the following remains constant when α varies = ?


The eccentricity of the hyperbola x2 – 3y2 = 2x + 8 is ______.


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