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
The parabola y2 = kx passes through the point (4, -2). Find its latus rectum and focus.
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
y2 = 20x
The average variable cost of the monthly output of x tonnes of a firm producing a valuable metal is ₹ `1/5`x2 – 6x + 100. Show that the average variable cost curve is a parabola. Also, find the output and the average cost at the vertex of the parabola.
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 which is symmetrical about x-axis and passing through (–2, –3).
The distance between directrix and focus of a parabola y2 = 4ax is:
Find the equation of the ellipse in the cases given below:
Foci `(+- 3, 0), "e"+ 1/2`
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 vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 = 16x
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 – 4y – 8x + 12 = 0
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 - y^2/144` = 1
Prove that the length of the latus rectum of the hyperbola `x^2/"a"^2 - y^2/"b"^2` = 1 is `(2"b"^2)/"a"`
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
Choose the correct alternative:
If P(x, y) be any point on 16x2 + 25y2 = 400 with foci F(3, 0) then PF1 + PF2 is
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:
