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
Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x – 3y + 2 = 0.
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 equation of the parabola which is symmetrical about x-axis and passing through (–2, –3).
The eccentricity of the parabola is:
The double ordinate passing through the focus is:
The equation of directrix of the parabola y2 = -x is:
Find the equation of the parabola in the cases given below:
Focus (4, 0) and directrix x = – 4
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 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 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 vertex, focus, equation of directrix and length of the latus rectum of the following:
x2 = 24y
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 = – 8x
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`y^2/16 - x^2/9` = 1
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
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
