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
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.
Find the axis, vertex, focus, equation of directrix and the length of latus rectum of the parabola (y - 2)2 = 4(x - 1)
The eccentricity of the parabola is:
The double ordinate passing through the focus is:
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 parabola in the cases given below:
Vertex (1, – 2) and Focus (4, – 2)
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 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
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
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:
