Advertisements
Advertisements
प्रश्न
Find the equation of the hyperbola in the cases given below:
Passing through (5, – 2) and length of the transverse axis along x-axis and of length 8 units
Advertisements
उत्तर
Transverse axis along x-axis
`x%2/"a"^2 - y^2/"b"^2` = 1
Length of transverse axis 2a = 8
⇒ a = 4
`x^2/16 - y^2/"b"^2` = 1
At (5, – 2) `25/16 - 4/"b"^2` = 1
`25/16 - 1 = 4/"b"^2`
`(25 - 16)/16 = 4/"b"^2`
⇒ `9/16 = 4/"b"^2`
b2 = `(16 xx 4)/9` = 4
Equation of hyperbola `x^2/16 - y^2/(64/9)` = 1
`x%^2/16 - (9y^2)/64` = 1
APPEARS IN
संबंधित प्रश्न
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = 8y
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = - 16y
The profit ₹ y accumulated in thousand in x months is given by y = -x2 + 10x – 15. Find the best time to end the project.
Find the equation of the parabola in the cases given below:
Passes through (2, – 3) and symmetric about y-axis
Find the equation of the parabola in the cases given below:
Vertex (1, – 2) and Focus (4, – 2)
Find the equation of the parabola in the cases given below:
End points of latus rectum (4, – 8) and (4, 8)
Find the equation of the ellipse in the cases given below:
Foci (0, ±4) and end points of major axis are (0, ±5)
Find the equation of the ellipse in the cases given below:
Length of latus rectum 4, distance between foci `4sqrt(2)`, centre (0, 0) and major axis as y-axis
Find the equation of the hyperbola in the cases given below:
Foci (± 2, 0), Eccentricity = `3/2`
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
x2 = 24y
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 + y^2/9` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`y^2/16 - x^2/9` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(x - 3)^2/225 + (y - 4)^2/289` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(y - 2)^3/25 + (x + 1)^2/16` = 1
Choose the correct alternative:
The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is
Which statement best describes a focal chord in any conic section?
The fixed straight line used in the definition of a conic section is called the:
A chord passing through any point on the conic and perpendicular to the axis is called:
