Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
e = `3/5`
Latus rectum `(2"b"^2)/"a"` = 8
b2 = `"a"^2(1 -"e"^2)`
4a = `"a"^2 (1 - 9/25)`
4 = `"a"(16/25)`
⇒ `25/4` = a
a2 = `625/16`
∴ b2 = 4a
= `4(25/4)` = 25
∴ Equation of Ellipse `x^2/"a"^2 + y^2/"b"^2` = 1
⇒ `(16x^2)/625 + y^2/25` = 1
APPEARS IN
संबंधित प्रश्न
The parabola y2 = kx passes through the point (4, -2). Find its latus rectum and focus.
Find the vertex, focus, axis, directrix, and the length of the latus rectum of the parabola y2 – 8y – 8x + 24 = 0.
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 which is symmetrical about x-axis and passing through (–2, –3).
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 distance between directrix and focus of a parabola y2 = 4ax is:
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 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 – 4y – 8x + 12 = 0
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:
`(y - 2)^3/25 + (x + 1)^2/16` = 1
Choose the correct alternative:
If P(x, y) be any point on 16x2 + 25y2 = 400 with foci F(3, 0) then PF1 + PF2 is
Which statement best describes a focal chord in any conic section?
The latus-rectum of a conic section is:
The fixed straight line used in the definition of a conic section is called the:
A chord passing through any point on the conic and perpendicular to the axis is called:
