Maharashtra State BoardHSC Science (Electronics) 11th
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Answer the following: Find the (i) lengths of the principal axes (ii) co-ordinates of the foci (iii) equations of directrices (iv) length of the latus rectum (v) Distance between foci (vi) distance b - Mathematics and Statistics

Sum

Answer the following:

Find the
(i) lengths of the principal axes
(ii) co-ordinates of the foci
(iii) equations of directrices
(iv) length of the latus rectum
(v) Distance between foci
(vi) distance between directrices of the curve

x2 − y2 = 16

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Solution

Given equation of the hyperbola is x2 – y2 = 16

∴ `x^2/16 - y^2/16` = 1

Comparing this equation with `x^2/"a"^2 - y^2/"b"^2` = 1, we get

a2 = 16 and b2 = 16

∴ a = 4 and b = 4

i. Length of transverse axis = 2a = 2(4) = 8

Length of conjugate axis = 2b = 2(4) = 8

ii. We know that

e =`sqrt("a"^2 + "b"^2)/"a"`

= `sqrt(16 + 16)/4`

= `sqrt(32)/4`

= `(4sqrt(2))/4`

= `sqrt(2)`

Co-ordinates of foci are S(ae, 0) and S'(– ae, 0),

i.e., `"S"(4sqrt(2), 0)` and `"S""'"(-4 sqrt(2), 0)`

iii. Equations of the directrices are x = `± "a"/"e"`.

∴ x = `± 4/sqrt(2)`

∴ x = `±2sqrt(2)`

iv. Length of latus rectum = `(2"b"^2)/"a"`

= `(2(16))/4`

= 8

v. Distance between foci = 2ae = `2(4)(sqrt(2)) = 8sqrt(2)`

vi. Distance between directrices = `(2"a")/"e"`

= `(2(4))/sqrt(2)`

= `4sqrt(2)`.

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 7 Conic Sections
Miscellaneous Exercise 7 | Q II. (13) (iv) | Page 178
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