# 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

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

#### 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).

Is there an error in this question or solution?

#### 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