Advertisements
Advertisements
प्रश्न
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/3 + y^2/10` = 1
Advertisements
उत्तर
It is an ellipse.
The major axis is along y-axis
a2 = 10, b2 = 3
a = `sqrt(10)`, b = `sqrt(3)`
c2 = a2 – b2
= 10 – 3
= 7
c = `sqrt(7)`
ae = `sqrt(7)`
`sqrt(10) = sqrt(7)`
e = `sqrt(7/10)`
(a) Centre (0, 0)
(b) Vertex (0, ± a) = `(0, +- sqrt(10))`
(c) Foci (0, ± c) – `(0, +- sqrt(7))`
(d) Equation of the directrix a
y = `+- "a"/"e"`
= `+- sqrt(10)/sqrt(7) * sqrt(10)`
= `+- 10/sqrt(7)`
y = `+- 10/sqrt(7)`
APPEARS IN
संबंधित प्रश्न
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
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = - 16y
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 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 ellipse in the cases given below:
Foci `(+- 3, 0), "e"+ 1/2`
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:
x2 – 2x + 8y + 17 = 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 - 3)^2/225 + (y - 4)^2/289` = 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 x + y = k is a normal to the parabola y2 = 12x, then the value of k is 14
