Advertisements
Advertisements
प्रश्न
find the equation of the hyperbola satisfying the given condition:
vertices (± 7, 0), \[e = \frac{4}{3}\]
Advertisements
उत्तर
The vertices of hyperbola are \[\left( \pm 7, 0 \right)\] and eccentricity is \[\frac{4}{3}\] Thus, the value of \[a = 7\].
Now, using the relation
\[b^2 = a^2 ( e^2 - 1)\], we get:
\[\Rightarrow b^2 = 49\left( \frac{16}{9} - 1 \right)\]
\[ \Rightarrow b^2 = 49 \times \frac{7}{9} = \frac{343}{9}\]
Thus, the equation of the hyperbola is
APPEARS IN
संबंधित प्रश्न
Find the equation of the hyperbola satisfying the given conditions:
Foci `(+-3sqrt5, 0)`, the latus rectum is of length 8.
Find the equation of the hyperbola satisfying the given conditions:
Foci `(0, +- sqrt10)`, passing through (2, 3)
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 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 (2, −1), directrix is 2x + 3y = 1 and eccentricity = 2 .
Find the equation of the hyperbola whose focus is (a, 0), directrix is 2x − y + a = 0 and eccentricity = \[\frac{4}{3}\].
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, 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 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 whose foci at (± 2, 0) and eccentricity is 3/2.
Find the equation of the hyperboala whose focus is at (4, 2), centre at (6, 2) and e = 2.
If P is any point on the hyperbola whose axis are equal, prove that SP. S'P = CP2.
Find the equation of the hyperbola satisfying the given condition :
vertices (± 2, 0), foci (± 3, 0)
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, ± \[\sqrt{10}\], 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.
The foci of the hyperbola 2x2 − 3y2 = 5 are
Find the equation of the hyperbola with vertices at (0, ± 6) and e = `5/3`. Find its foci.
Find the equation of the hyperbola whose vertices are (± 6, 0) and one of the directrices is x = 4.
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 ______.
Find the eccentricity of the hyperbola 9y2 – 4x2 = 36.
Find the equation of the hyperbola with eccentricity `3/2` and foci at (± 2, 0).
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 equation of the hyperbola with vertices at (0, ± 6) and eccentricity `5/3` is ______ and its foci are ______.
The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half of the distance between the foci is ______.
