Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x – 3y + 2 = 0.
The parabola y2 = kx passes through the point (4, -2). Find its latus rectum and focus.
Find the vertex, focus, axis, directrix, and the length of the latus rectum of the parabola y2 – 8y – 8x + 24 = 0.
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:
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:
Length of latus rectum 8, eccentricity = `3/5` centre (0, 0) and major axis on x-axis
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
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 + y^2/9` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/3 + y^2/10` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 - y^2/144` = 1
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`y^2/16 - x^2/9` = 1
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
Choose the correct alternative:
If P(x, y) be any point on 16x2 + 25y2 = 400 with foci F(3, 0) then PF1 + PF2 is
