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 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.
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = 8y
The distance between directrix and focus of a parabola y2 = 4ax is:
Find the equation of the parabola in the cases given below:
Focus (4, 0) and directrix x = – 4
Find the equation of the parabola in the cases given below:
End points of latus rectum (4, – 8) and (4, 8)
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:
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 = 16x
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^2/9` = 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"`
Choose the correct alternative:
If x + y = k is a normal to the parabola y2 = 12x, then the value of k is 14
Which statement best describes a focal chord in any conic section?
The fixed straight line used in the definition of a conic section is called the:
