Advertisements
Advertisements
प्रश्न
Find the equations of the tangents to the hyperbola `x^2/25 - y^2/9` = 1 making equal intercepts on the co-ordinate axes
Advertisements
उत्तर
Given equation of the hyperbola is `x^2/25 - y^2/9` = 1.
Comparing this equation with `x^2/"a"^2 - y^2/"b"^2` = 1, we get
a2 = 25 and b2 = 9
Since the tangents make equal intercepts on the co-ordinate axes, m = – 1.
Equations of tangents to the hyperbola
`x^2/"a"^2 - y^2/"b"^2` = 1 having slope m are
y = `"m"x ± sqrt("a"^2"m"^2 - "b"^2)`
∴ y = `-x ± sqrt(25(-1)^2 - 9)`
∴ y = `-x ± sqrt(16)`
∴ x + y = ± 4.
APPEARS IN
संबंधित प्रश्न
Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:
`x^2/25 - y^2/16` = – 1
Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:
16x2 – 9y2 = 144
Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:
21x2 – 4y2 = 84
Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:
x2 – y2 = 16
Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:
`y^2/25 - x^2/9` = 1
Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:
`y^2/25 - x^2/144` = 1
Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola:
x = 2 sec θ, y = `2sqrt(3) tan theta`
Find the eccentricity of the hyperbola, which is conjugate to the hyperbola x2 – 3y2 = 3
Find the equation of the hyperbola referred to its principal axes:
whose distance between foci is 10 and eccentricity `5/2`
Find the equation of the hyperbola referred to its principal axes:
whose distance between foci is 10 and length of conjugate axis 6
Find the equation of the hyperbola referred to its principal axes:
whose distance between directrices is `8/3` and eccentricity is `3/2`
Find the equation of the hyperbola referred to its principal axes:
whose vertices are (± 7, 0) and end points of conjugate axis are (0, ±3)
Find the equation of the hyperbola referred to its principal axes:
whose length of transverse and conjugate axis are 6 and 9 respectively
Find the equation of the tangent to the hyperbola:
3x2 – 4y2 = 12 at the point (4, 3)
Find the equation of the tangent to the hyperbola:
`x^2/144 - y^2/25` = 1 at the point whose eccentric angle is `pi/3`
Find the equation of the tangent to the hyperbola:
`x^2/16 - y^2/9` = 1 at the point in a first quadratures whose ordinate is 3
Select the correct option from the given alternatives:
Eccentricity of the hyperbola 16x2 − 3y2 − 32x − 12y − 44 = 0 is
Select the correct option from the given alternatives:
If the line 2x − y = 4 touches the hyperbola 4x2 − 3y2 = 24, the point of contact is
Select the correct option from the given alternatives:
The foci of hyperbola 4x2 − 9y2 − 36 = 0 are
Answer the following:
Find the equation of the hyperbola in the standard form if Length of conjugate axis is 5 and distance between foci is 13.
Answer the following:
Find the equation of the hyperbola in the standard form if eccentricity is `3/2` and distance between foci is 12.
Answer the following:
Find the equation of the tangent to the hyperbola 7x2 − 3y2 = 51 at (−3, −2)
Answer the following:
Find the equation of the tangent to the hyperbola x = 3 secθ, y = 5 tanθ at θ = `pi/3`
Answer the following:
Find the equation of the tangent to the hyperbola `x^2/25 − y^2/16` = 1 at P(30°)
Answer the following:
Find the equations of the tangents to the hyperbola 3x2 − y2 = 48 which are perpendicular to the line x + 2y − 7 = 0
If P(x1, y1) is a point on the hyperbola x2 - y2 = a2, then SP. S'P = ______.
Let H: `x^2/a^2 - y^2/b^2` = 1, a > 0, b > 0, be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is `4(2sqrt(2) + sqrt(14))`. If the eccentricity H is `sqrt(11)/2`, then the value of a2 + 2b2 is equal to ______.
A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola `x^2/4 - y^2/2` = 1 at the point (x1, y1). Then `x_1^2 + 5y_1^2` is equal to ______.
(x – 1)2 + (y – 2)2 = `(3(2x + 3y + 2)^2)/13`represents hyperbola whose eccentricity is ______.
The hyperbola `x^2/a^2 - y^2/b^2` = 1 passes through the point of intersection of the lines `x - 3sqrt(5)y` = 0 and `sqrt(5)x - 2y` = 13 and the length of its latus rectum is `4/3` units. The coordinates of its focus are ______.
The locus of the mid-point of the chords of the hyperbola `(x^2/a^2) - (y^2/b^2)` = 1 passing through a fixed point (α, β) is a hyperbola with centre at `(α/2, β/2)` It equation is ______.
For the Hyperbola `x^2/(cos^2α) - y^2/(sin^2α)` = 1, which of the following remains constant when α varies = ?
