Advertisements
Advertisements
प्रश्न
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 = 16x
Advertisements
उत्तर
4a = 16
a = 4
(a) Vertex V(0, 0)
(b) Focus S(a, 0) = S(4, 0)
(c) Equation of the directrix x = – a
x = – 4
⇒ x + 4 = 0
(d) Length of the latus rectum = 4a
= 4(4)
= 16
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 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 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 focus of the parabola x2 = 16y is:
The double ordinate passing through the focus 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:
End points of latus rectum (4, – 8) and (4, 8)
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:
Centre (2, 1), one of the foci (8, 1) and corresponding directrix x = 4
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:
x2 = 24y
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 - y^2/144` = 1
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
