Advertisements
Advertisements
प्रश्न
Find the equation of the ellipse in the cases given below:
Foci (0, ±4) and end points of major axis are (0, ±5)
Advertisements
उत्तर
Foci (0, ±c) = (0, +4)
Vertex (0, ±a) = (0, ±5)
∴ c = 4, a = 5
ae = 4
5e = 4
e = `4/5`
b2 = a2 – c2
= 25 – 16
b2 = 9
Equation of the ellipse be `x^2/"b"^2 + y^2/"a"^2` = 1
`x^2/9 + y^2/25` = 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.
The parabola y2 = kx passes through the point (4, -2). Find its latus rectum and focus.
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
y2 = 20x
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:
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 hyperbola in the cases given below:
Centre (2, 1), one of the foci (8, 1) and corresponding directrix x = 4
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 – 4y – 8x + 12 = 0
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:
`y^2/16 - x^2/9` = 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:
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 P(x, y) be any point on 16x2 + 25y2 = 400 with foci F(3, 0) then PF1 + PF2 is
Choose the correct alternative:
If x + y = k is a normal to the parabola y2 = 12x, then the value of k is 14
