Advertisements
Advertisements
प्रश्न
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 + y^2/9` = 1
उत्तर
It is of the form `x^2/25 + y^2/9` = 1
which is an ellipse
Here a2 = 25, b2 = 9
a = 5, b = 3
e2 = `("a"^2 - "b"^2)/"a"^2`
= `(25 - 9)/25`
= `16/25`
⇒ e = `4/5`
Now e = `4/5` and a = 5
⇒ ae = 4 and `"a"/"e" = 5/(4/5) = 25/4`
Here the major axis is along x axis
∴ Centre = (0, 0)
Foci = (± ae, 0) = (± 4, 0)
Vertices = (± a, 0) = (±5, 0)
Equation of directrix x = `+- "a"/"e"`
(i.e,) x = `+- 25/4`
APPEARS IN
संबंधित प्रश्न
The parabola y2 = kx passes through the point (4, -2). Find its latus rectum and focus.
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 eccentricity of the parabola is:
The double ordinate passing through the focus 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 `(+- 3, 0), "e"+ 1/2`
Find the equation of the hyperbola in the cases given below:
Foci (± 2, 0), Eccentricity = `3/2`
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:
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
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 + 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:
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
