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 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.
The focus of the parabola x2 = 16y is:
The eccentricity of the parabola is:
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:
Passes through (2, – 3) and symmetric about y-axis
Find the equation of the ellipse in the cases given below:
Foci `(+- 3, 0), "e"+ 1/2`
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
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"`
Show that the absolute value of difference of the focal distances of any point P on the hyperbola is the length of its transverse axis
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:
`(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
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
Which statement best describes a focal chord in any conic section?
