Advertisements
Advertisements
प्रश्न
Answer the following:
Find the equation of the hyperbola in the standard form if eccentricity is `3/2` and distance between foci is 12.
Advertisements
उत्तर
Let the required equation of hyperbola be `x^2/"a"^2 - y^2/"b"^2` = 1
Given, eccentricity (e) = `3/2`
Distance between foci = 2ae
Given, distance between foci = 12
∴ 2ae = 12
∴ `2"a"(3/2)` = 12
∴ 3a = 12
∴ a = `12/3` = 4
∴ a2 = 16
Now, b2 = a2(e2 – 1)
∴ b2 = `16[(3/2)^2 - 1]`
= `16(9/4 - 1)`
= `16(5/4)`
∴ b2 = 20
∴ The required equation of hyperbola is `x^2/16 - y^2/20` = 1.
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:
`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:
`y^2/25 - x^2/144` = 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 equation of the hyperbola referred to its principal axes:
whose distance between foci is 10 and eccentricity `5/2`
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 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 tangent to the hyperbola:
3x2 – 4y2 = 12 at the point (4, 3)
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
Find the equation of the tangent to the hyperbola:
9x2 – 16y2 = 144 at the point L of latus rectum in the first quadrant
Show that the line 3x – 4y + 10 = 0 is tangent till the hyperbola x2 – 4y2 = 20. Also find the point of contact
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:
Eccentricity of the hyperbola 16x2 − 3y2 − 32x − 12y − 44 = 0 is
Select the correct option from the given alternatives:
The foci of hyperbola 4x2 − 9y2 − 36 = 0 are
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 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 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
If P(x1, y1) is a point on the hyperbola x2 - y2 = a2, then SP. S'P = ______.
The asymptotes of the hyperbola xy = hx + ky are ______.
Parametric form of the hyperbola `x^2/4 - y^2/9` = –1 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 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?
Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola `x^2/"a"^2 - "y"^2/"b"^2` = 1. Let e' and l' respectively the eccentricity and length of the latus rectum of its conjugate hyperbola. If e2 = `11/14"l'"` and (e')2 = `11/8"l"^'` then the value of 77a + 44b is equal to ______.
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 ______.
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 ______.
