Advertisements
Advertisements
प्रश्न
Find the equation of the ellipse in the cases given below:
Foci `(+- 3, 0), "e"+ 1/2`
Advertisements
उत्तर
Foci (± c, 0) = (± 3, 0)
e = `1/2`
c = ae = 3
`"a"(1/2)` = 3
a = 6 ⇒ a² = 36
b2 = a2 – c2
b2 = 36 – 9 = 27
b2 = 27
Equation of the ellipse be `x^2/"a"^2 + y^2/"b"^2` = 1
`x^2/36 + y^2/27` = 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.
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).
The eccentricity of the parabola is:
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 parabola in the cases given below:
Vertex (1, – 2) and Focus (4, – 2)
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:
Foci (± 2, 0), Eccentricity = `3/2`
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
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:
9x2 – y2 – 36x – 6y + 18 = 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
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:
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:
