Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
The parabola y2 = kx passes through the point (4, -2). Find its latus rectum and focus.
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.
The eccentricity of the parabola 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 hyperbola in the cases given below:
Centre (2, 1), one of the foci (8, 1) and corresponding directrix x = 4
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 + y^2/9` = 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:
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:
The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is
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:
