Advertisements
Advertisements
प्रश्न
The difference of the focal distances of any point on the hyperbola is equal to
विकल्प
length of the conjugate axis
eccentricity
length of the transverse axis
Latus-rectum
उत्तर
length of the transverse axis
Let \[P\left( x, y \right)\] be any point on the hyperbola, and \[S, S'\] be the focus with coordinates \[\left( \pm ae, 0 \right)\] .
⇒ \[S'P - SP = 2a\]
Thus, the difference of the focal distances of any point on the hyperbola is equal to the length of the transverse axis.
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 `(+-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 (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 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 .
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, referred to its principal axes as axes of coordinates, in the conjugate axis is 7 and passes through the point (3, −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 at (0 ± 7) and foci at \[\left( 0, \pm \frac{28}{3} \right)\] .
Find the equation of the hyperboala whose focus is at (5, 2), vertex at (4, 2) and centre at (3, 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, ± 5), foci (0, ± 8)
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
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).
The foci of the hyperbola 9x2 − 16y2 = 144 are
The equation of the hyperbola whose foci are (6, 4) and (−4, 4) and eccentricity 2, is
The equation of the hyperbola whose centre is (6, 2) one focus is (4, 2) and of 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 ______.
Find the eccentricity of the hyperbola 9y2 – 4x2 = 36.
Find the equation of the hyperbola with eccentricity `3/2` and foci at (± 2, 0).
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 represent a hyperbola.
Find the equation of the hyperbola with vertices (0, ± 7), e = `4/3`
Find the equation of the hyperbola with foci `(0, +- sqrt(10))`, passing through (2, 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 equation of the hyperbola with vertices at (0, ± 6) and eccentricity `5/3` is ______ and its foci are ______.
