Advertisements
Advertisements
प्रश्न
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(y - 2)^3/25 + (x + 1)^2/16` = 1
Advertisements
उत्तर
It is a hyperbola.
The transverse axis is parallel to y axis.
a2 = 25, b2 = 16
a = ± 5, b = 4
c2 = a2 + b2
= 25 + 16
= 41
c = `sqrt(41)`
ae = `sqrt(41)`
5e = `sqrt(41)`
e = `sqrt(41)/5`
Centre (h, k) = (– 1, 2)
Vertices (h, ± a + k) = (– 1, ± 5 + 2)
= (– 1, 5 + 2) and (– 1, – 5 + 2)
= (– 1, 7) and (– 1, – 3)
Foci (h, ± c + k) = `(- 1 +- sqrt(41) + 2)`
= `(-1, sqrt(41) + 2)` and `(-1, - sqrt(41) + 2)`
Directrix x = `+- "a"/"e" + "k"`
= `+- 5/(sqrt(41)/5) + 2`
= `+- 25/sqrt(41) + 2`
y = `25/sqrt(41) + 2` and y = `- 25/sqrt(41) + 2`
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
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 = 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.
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:
Foci `(+- 3, 0), "e"+ 1/2`
Find the equation of the ellipse in the cases given below:
Foci (0, ±4) and end points of major axis are (0, ±5)
Find the equation of the ellipse in the cases given below:
Length of latus rectum 8, eccentricity = `3/5` centre (0, 0) and major axis on x-axis
Find the equation of the hyperbola in the cases given below:
Foci (± 2, 0), Eccentricity = `3/2`
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 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 = – 8x
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 – 4y – 8x + 12 = 0
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:
18x2 + 12y2 – 144x + 48y + 120 = 0
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
