Advertisements
Advertisements
Question
Find the equation of the hyperbola whose vertices are (± 6, 0) and one of the directrices is x = 4.
Advertisements
Solution
As the vertices are on the x-axis and their middle point is the origin
The equation is of the type `x^2/a^2 - y^2/b^2` = 1.
Here b2 = a2(e2 – 1)
Vertices are (± a, 0)
And Directrices are given by x = `+- a/e`.
Thus `a= 6, a/e` = 4
And so e = `3/2`
Which gives b2 = `36 9/4 - 1` = 45
Consequently, the required equation of the hyperbola is `x^2/36 - y^2/45` = 1
APPEARS IN
RELATED QUESTIONS
Find the equation of the hyperbola satisfying the given conditions:
Vertices (0, ±5), foci (0, ±8)
Find the equation of the hyperbola satisfying the given conditions:
Vertices (0, ±3), foci (0, ±5)
Find the equation of the hyperbola satisfying the given conditions:
Foci (±5, 0), the transverse axis is of length 8.
Find the equation of the hyperbola satisfying the given conditions:
Foci (0, ±13), the conjugate axis is of length 24.
The equation of the directrix of a hyperbola is x − y + 3 = 0. Its focus is (−1, 1) and eccentricity 3. Find the equation of the hyperbola.
Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .
9x2 − 16y2 = 144
Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .
16x2 − 9y2 = −144
Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .
4x2 − 3y2 = 36
Find the eccentricity, coordinates of the foci, equation of directrice and length of the latus-rectum of the hyperbola .
2x2 − 3y2 = 5.
Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the distance between the foci = 16 and eccentricity = \[\sqrt{2}\].
Find the equation of the hyperbola whose foci are (6, 4) and (−4, 4) and eccentricity is 2.
Find the equation of the hyperbola whose vertices are (−8, −1) and (16, −1) and focus is (17, −1).
Find the equation of the hyperbola whose foci are (4, 2) and (8, 2) and eccentricity is 2.
Find the equation of the hyperbola whose vertices are at (0 ± 7) and foci at \[\left( 0, \pm \frac{28}{3} \right)\] .
Find the equation of the hyperbola whose foci at (± 2, 0) and eccentricity is 3/2.
find the equation of the hyperbola satisfying the given condition:
vertices (± 7, 0), \[e = \frac{4}{3}\]
Find the equation of the hyperbola satisfying the given condition:
foci (0, ± \[\sqrt{10}\], passing through (2, 3).
Show that the set of all points such that the difference of their distances from (4, 0) and (− 4,0) is always equal to 2 represents a hyperbola.
Write the distance between the directrices of the hyperbola x = 8 sec θ, y = 8 tan θ.
Write the equation of the hyperbola whose vertices are (± 3, 0) and foci at (± 5, 0).
Equation of the hyperbola whose vertices are (± 3, 0) and foci at (± 5, 0), is
The equation of the hyperbola whose foci are (6, 4) and (−4, 4) and eccentricity 2, is
The length of the transverse axis along x-axis with centre at origin of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is ______.
The eccentricity of the hyperbola `x^2/a^2 - y^2/b^2` = 1 which passes through the points (3, 0) and `(3 sqrt(2), 2)` is ______.
If the distance between the foci of a hyperbola is 16 and its eccentricity is `sqrt(2)`, then obtain the equation of the hyperbola.
Find the equation of the hyperbola with eccentricity `3/2` and foci at (± 2, 0).
Find the equation of the hyperbola with vertices (± 5, 0), foci (± 7, 0)
Find the equation of the hyperbola with vertices (0, ± 7), e = `4/3`
The locus of the point of intersection of lines `sqrt(3)x - y - 4sqrt(3)k` = 0 and `sqrt(3)kx + ky - 4sqrt(3)` = 0 for different value of k is a hyperbola whose eccentricity is 2.
The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half of the distance between the foci is ______.
