Advertisements
Advertisements
Question
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`(x + 3)^2/225 + (y - 4)^2/64` = 1
Advertisements
Solution
It is an hyperbola.
The transverse axis is parallell to x axis.
a2= 225, b2 = 64
a = 15, b = 8
c2 = a2 – b2
= 225 + 64
c2 = 289
c = 17
ae = 17
5e = 17
e = `17/15`
Centre (h, k) = (– 3, 4)
Vertices (h ± a, k) = (– 3 ± 15, 4)
= (– 3 + 15, 4) and (– 3 – 15, 4)
= (12, 4) and (– 18, 4)
Foci (h ± c, k) = (– 3 ± 17, 4)
= (– 3 + 17, 4) and (– 3 – 17, 4)
= (14, 4) and (– 20, 4)
Directrix x = `+- "a"/"e" + "h"`
= `+- 15/(17/5) - 3`
= `+- 225/17 - 3`
x = `225/17 - 3` and x = `- 225/17 - 3`
= `174/17` and = `(- 276)/17`
APPEARS IN
RELATED QUESTIONS
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 profit ₹ y accumulated in thousand in x months is given by y = -x2 + 10x – 15. Find the best time to end the project.
The distance between directrix and focus of a parabola y2 = 4ax is:
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:
x2 – 2x + 8y + 17 = 0
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
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:
9x2 – y2 – 36x – 6y + 18 = 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
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:
A chord passing through any point on the conic and perpendicular to the axis is called:
