Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
Distance CS = ae = 6 .......(1)
Directrix `"a"/x` = 4 .......(2)
(1) × (2)
⇒ ae × `"a"/"e"` = 24
a2 = 24
∴ c = ae = 6
b2 = c2 – a2
= 36 – 24 = 12
The transverse axis is parallel to x-axis
∴ `(x - "h")^2/"a"^2 - (y - "k")^2/"b"^2` = 1(h, k) = (2, 1)
`(x - 2)^2/24 - (y - 1)^2/12` = 1
APPEARS IN
संबंधित प्रश्न
Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x – 3y + 2 = 0.
Find the vertex, focus, axis, directrix, and the length of the latus rectum of the parabola y2 – 8y – 8x + 24 = 0.
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 equation of the parabola which is symmetrical about x-axis and passing through (–2, –3).
The equation of directrix of the parabola y2 = -x is:
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 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 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 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
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 = – 8x
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 - y^2/144` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
18x2 + 12y2 – 144x + 48y + 120 = 0
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 x + y = k is a normal to the parabola y2 = 12x, then the value of k is 14
The latus-rectum of a conic section is:
The fixed straight line used in the definition of a conic section is called the:
