Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
The profit ₹ y accumulated in thousand in x months is given by y = -x2 + 10x – 15. Find the best time to end the project.
The eccentricity of the parabola is:
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 (0, ±4) and end points of major axis are (0, ±5)
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:
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:
x2 = 24y
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^2/144` = 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 - 3)^2/225 + (y - 4)^2/289` = 1
Choose the correct alternative:
If x + y = k is a normal to the parabola y2 = 12x, then the value of k is 14
The fixed straight line used in the definition of a conic section is called the:
If the eccentricity e > 1, the conic section is:
A chord passing through any point on the conic and perpendicular to the axis is called:
