Advertisements
Advertisements
प्रश्न
Find the equation of the hyperbola with vertices (± 5, 0), foci (± 7, 0)
उत्तर
Given that vertices (± 5, 0), foci (± 7, 0)
Vertex of hyperbola = (± a, 0) and foci (± ae, 0)
∴ a = 5 and ae = 7
⇒ 5 × e = 7
⇒ e = `7/5`
Now b2 = a2(e2 – 1)
⇒ b2 = `25(49/25 - 1)`
⇒ b2 = `25 xx 24/25`
⇒ b2 = 24
The equation of the hyperbola is `x^2/25 - y^2/24` = 1
APPEARS IN
संबंधित प्रश्न
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 whose focus is (0, 3), directrix is x + y − 1 = 0 and eccentricity = 2 .
Find the equation of the hyperbola whose focus is (1, 1), directrix is 3x + 4y + 8 = 0 and eccentricity = 2 .
Find the equation of the hyperbola whose focus is (2, −1), directrix is 2x + 3y = 1 and eccentricity = 2 .
Find the equation of the hyperbola whose focus is (2, 2), directrix is x + y = 9 and eccentricity = 2.
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 equation of the hyperbola, referred to its principal axes as axes of coordinates, in the conjugate axis is 5 and the distance between foci = 13 .
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 vertices are at (0 ± 7) and foci at \[\left( 0, \pm \frac{28}{3} \right)\] .
Find the equation of the hyperbola whose vertices are at (± 6, 0) and one of the directrices is x = 4.
Find the equation of the hyperbola satisfying the given condition :
vertices (0, ± 3), foci (0, ± 5)
Find the equation of the hyperbola satisfying the given condition :
foci (0, ± 13), conjugate axis = 24
Find the equation of the hyperbola satisfying the given condition:
foci (0, ± \[\sqrt{10}\], passing through (2, 3).
The equation of the hyperbola whose foci are (6, 4) and (−4, 4) and eccentricity 2, is
The foci of the hyperbola 2x2 − 3y2 = 5 are
The equation of the hyperbola whose centre is (6, 2) one focus is (4, 2) and of eccentricity 2 is
Find the equation of the hyperbola with vertices at (0, ± 6) and e = `5/3`. Find its foci.
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 eccentricity of the hyperbola 9y2 – 4x2 = 36.
Find the equation of the hyperbola with vertices (0, ± 7), e = `4/3`
The equation of the hyperbola with vertices at (0, ± 6) and eccentricity `5/3` is ______ and its foci are ______.
