Advertisements
Advertisements
Question
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
x2 = 24y
Advertisements
Solution
(a) Vertex V(0, 0)
(b) Focus S (0, a) = S(0, 6)
(c) Equation of the directrix y = – a = – 6
⇒ y + 6 = 0
(d) Length of the latus rectum = 4a
= 4(6)
= 24
APPEARS IN
RELATED QUESTIONS
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
y2 = 20x
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).
Find the axis, vertex, focus, equation of directrix and the length of latus rectum of the parabola (y - 2)2 = 4(x - 1)
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
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)^2/64` = 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
Which statement best describes a focal chord in any conic section?
The latus-rectum of a conic section is:
If the eccentricity e > 1, the conic section is:
