Advertisements
Advertisements
प्रश्न
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
उत्तर
Let P be a point on the hyperbola.
Definition of conic
`"SP"/"PM"` = e
`"S'P"/"PM'"` = e
SP = e(PM) ……..(1)
S’P = e (PM’) ……….(2)
(2) – (1)
⇒ S’P – SP = e PM’- e PM
= e(PM’ – PM)
= e MM’
= e ZZ’ .......[∵ MM’ = ZZ’ = `(2"a")/"e"`]
= `"e"((2"a")/"e")`
S’P – SP = 2a .......(constant)
= length of the transverse axis.
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 vertex, focus, axis, directrix, and the length of the latus rectum of the parabola y2 – 8y – 8x + 24 = 0.
Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola
x2 = 8y
The focus of the parabola x2 = 16y 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:
End points of latus rectum (4, – 8) and (4, 8)
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:
Foci (± 2, 0), Eccentricity = `3/2`
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:
`x^2/25 - y^2/144` = 1
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:
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
