Advertisements
Advertisements
प्रश्न
Select the correct option from the given alternatives:
The foci of hyperbola 4x2 − 9y2 − 36 = 0 are
विकल्प
`(± sqrt(13), 0)`
`(± sqrt(11), 0)`
`(± sqrt(12), 0)`
` (0,± sqrt(12))`
उत्तर
The foci of hyperbola 4x2 − 9y2 − 36 = 0 are `(± sqrt(13), 0)`
APPEARS IN
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:
3x2 – y2 = 4
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:
`y^2/25 - x^2/9` = 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 sec θ, y = `2sqrt(3) tan theta`
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 foci is 10 and length of conjugate axis 6
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:
whose vertices are (± 7, 0) and end points of conjugate axis are (0, ±3)
Find the equation of the hyperbola referred to its principal axes:
whose foci are at (±2, 0) and eccentricity `3/2`
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:
`x^2/144 - y^2/25` = 1 at the point whose eccentric angle is `pi/3`
Find the equation of the tangent to the hyperbola:
`x^2/16 - y^2/9` = 1 at the point in a first quadratures whose ordinate is 3
Select the correct option from the given alternatives
The eccentricity of rectangular hyperbola is
Select the correct option from the given alternatives:
Eccentricity of the hyperbola 16x2 − 3y2 − 32x − 12y − 44 = 0 is
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
Answer the following:
For the hyperbola `x^2/100−y^2/25` = 1, prove that SA. S'A = 25, where S and S' are the foci and A is the vertex
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 eccentricity is `3/2` and distance between foci is 12.
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 equation of the tangent to the hyperbola x = 3 secθ, y = 5 tanθ at θ = `pi/3`
Answer the following:
Find the equation of the tangent to the hyperbola `x^2/25 − y^2/16` = 1 at P(30°)
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 ______.
The foci of a hyperbola coincide with the foci of the ellipse `x^2/25 + y^2/9` = 1. Find the equation of the hyperbola, if its eccentricity is 2.
(x – 1)2 + (y – 2)2 = `(3(2x + 3y + 2)^2)/13`represents hyperbola whose eccentricity is ______.
The equation of conjugate axis for the hyperbola `(x + y + 1)^2/4 - (x - y + 2)^2/9` = 1 is ______.
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 e1 and e2 be the eccentricities of the ellipse, `x^2/25 + y^2/b^2` = 1 (b < 5) and the hyperbola, `x^2/16 - y^2/b^2` = 1 respectively satisfying e1e2 = 1. If α and β are the distances between the foci of the ellipse and the foci of the hyperbola respectively, then the ordered pair (α, β) is equal to ______.
The hyperbola `x^2/a^2 - y^2/b^2` = 1 passes through the point `(3sqrt(5), 1)` and the length of its latus rectum is `4/3` units. The length of the conjugate axis is ______.