Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
The focus of the parabola x2 = 16y is:
The eccentricity of the parabola is:
The equation of directrix of the parabola y2 = -x 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 equation of the hyperbola in the cases given below:
Foci (± 2, 0), Eccentricity = `3/2`
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:
y2 = 16x
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 = – 8x
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
x2 – 2x + 8y + 17 = 0
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^2/25 - 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)^2/64` = 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 x + y = k is a normal to the parabola y2 = 12x, then the value of k is 14
