Advertisements
Advertisements
प्रश्न
Find the equation of the hyperbola in the cases given below:
Passing through (5, – 2) and length of the transverse axis along x-axis and of length 8 units
Advertisements
उत्तर
Transverse axis along x-axis
`x%2/"a"^2 - y^2/"b"^2` = 1
Length of transverse axis 2a = 8
⇒ a = 4
`x^2/16 - y^2/"b"^2` = 1
At (5, – 2) `25/16 - 4/"b"^2` = 1
`25/16 - 1 = 4/"b"^2`
`(25 - 16)/16 = 4/"b"^2`
⇒ `9/16 = 4/"b"^2`
b2 = `(16 xx 4)/9` = 4
Equation of hyperbola `x^2/16 - y^2/(64/9)` = 1
`x%^2/16 - (9y^2)/64` = 1
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.
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 = - 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 which is symmetrical about x-axis and passing through (–2, –3).
The focus of the parabola x2 = 16y is:
The eccentricity of the parabola 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 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:
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 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
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"`
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
The fixed straight line used in the definition of a conic section is called the:
