Advertisements
Advertisements
Question
Find the equation of the hyperbola referred to its principal axes:
whose length of conjugate axis = 12 and passing through (1, – 2)
Advertisements
Solution
Let the equation of the hyperbola referred to principal axes be `x^2/"a"^2 - y^2/"b"^2` = 1 ...(1)
Length of conjugate axes = 2b = 12
∴ b = 6
The hyperbola passes through (1, – 2)
∴ `1^2/"a"^2 - (-2)^2/6^2` = 1 ........[∵ b = 6]
∴ `1/"a"^2 = 1 + 1/9 = 10/9`
∴ a2 = `9/10`
∴ by (1), the equation of the required hyperbola is `x^2/((9/10)) - y^2/36` = 1
∴ `(10x^2)/9 - y^2/36` = 1.
APPEARS IN
RELATED QUESTIONS
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:
21x2 – 4y2 = 84
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 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 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`
Show that the line 3x – 4y + 10 = 0 is tangent till the hyperbola x2 – 4y2 = 20. Also find the point of contact
If the 3x – 4y = k touches the hyperbola `x^2/5 - (4y^2)/5` = 1 then find the value of k
Find the equations of the tangents to the hyperbola `x^2/25 - y^2/9` = 1 making equal intercepts on the co-ordinate axes
Select the correct option from the given alternatives
The eccentricity of rectangular hyperbola 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 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 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°)
Answer the following:
Show that the line 2x − y = 4 touches the hyperbola 4x2 − 3y2 = 24. Find the point of contact
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 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 ______.
(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 equation of conjugate axis for the hyperbola `(x + y + 1)^2/4 - (x - y + 2)^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 ______.
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 = ?
