Advertisements
Advertisements
Question
The difference of the focal distances of any point on the hyperbola is equal to
Options
length of the conjugate axis
eccentricity
length of the transverse axis
Latus-rectum
Solution
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
RELATED QUESTIONS
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 `(+-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)
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, 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 .
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 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, 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 foci are (4, 2) and (8, 2) and eccentricity is 2.
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 (5, 2), vertex at (4, 2) and centre at (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 (0, ± 3), foci (0, ± 5)
Find the equation of the hyperbola satisfying the given condition :
foci (0, ± 13), conjugate axis = 24
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 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 ______.
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 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 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 ______.
The distance between the foci of a hyperbola is 16 and its eccentricity is `sqrt(2)`. Its equation is ______.
Equation of the hyperbola with eccentricty `3/2` and foci at (± 2, 0) is ______.
