Advertisements
Advertisements
प्रश्न
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`y^2/16 - x^2/9` = 1
Advertisements
उत्तर
It is Hyperbola.
The transverse axis the y axis
a2 = 16, b2 = 9
a = 4, b = 3
c2 = a2 + b2
= 16 + 6 = 25
c = 5
ae = 5
4e = 5
e = `5/4`
(a) Centre (0, 0)
(b) Vertex (0, ± a) = (0, ± 4)
(c) Foci (0, ± ae) = (0, ± 5)
(d) Equation of the directrix
y = `+- "a"/"e" = +- 4/(5/4) = +- 16/5`
y = `+- 16/5`
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 axis, vertex, focus, equation of directrix and the length of latus rectum of the parabola (y - 2)2 = 4(x - 1)
The focus of the parabola x2 = 16y is:
Find the equation of the parabola in the cases given below:
Focus (4, 0) and directrix x = – 4
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:
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:
Centre (2, 1), one of the foci (8, 1) and corresponding directrix x = 4
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:
`x^2/3 + y^2/10` = 1
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 + 1)^2/100 + (y - 2)^2/64` = 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
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
18x2 + 12y2 – 144x + 48y + 120 = 0
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
9x2 – y2 – 36x – 6y + 18 = 0
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 latus-rectum of a conic section is:
A chord passing through any point on the conic and perpendicular to the axis is called:
