Advertisements
Advertisements
प्रश्न
Find the equation of the hyperbola in the cases given below:
Foci (± 2, 0), Eccentricity = `3/2`
Advertisements
उत्तर
e = `3/2`
Foci (±c ,0) = (±2, 0)
c = 2
ae = 2
`a(3/2)` = 2
a = `4/3`, a2 = `16/9`
b2 = c2 – a2
= `4 - 16/9`
= `20/9`
Equation of hyperbola
`x^2/"a"^2 - y^2/"b"^2` = 1
`x^2/(16/9) - y^2/(20/9)` = 1
`(9x^2)/16 - (9y^2)/20` = 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
y2 = 20x
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = 8y
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 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:
Length of latus rectum 8, eccentricity = `3/5` centre (0, 0) and major axis on x-axis
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 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:
x2 = 24y
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 – 4y – 8x + 12 = 0
Show that the absolute value of difference of the focal distances of any point P on the hyperbola is the length of its transverse axis
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
18x2 + 12y2 – 144x + 48y + 120 = 0
Which statement best describes a focal chord in any conic section?
The latus-rectum of a conic section is:
The fixed straight line used in the definition of a conic section is called the:
If the eccentricity e > 1, the conic section is:
