Answer the following: Find the equation of the hyperbola in the standard form if Length of conjugate axis is 5 and distance between foci is 13 - Mathematics and Statistics

Sum

Find the equation of the hyperbola in the standard form if Length of conjugate axis is 5 and distance between foci is 13

Solution

Let the required equation of hyperbola be

x^2/"a"^2 - y^2/"b"^2 = 1

Length of conjugate axis = 2b

Given, length of conjugate axis = 5

∴ 2b = 5

∴ b = 5/2

∴ b2 = 25/4

Distance between foci = 2ae

Given, distance between foci = 13

∴ 2ae = 13

∴ ae = 13/2

∴ a2e2 = 169/4

∴ Now, b2 = a2(e2 – 1)

∴ b2 = a2e2 – a

∴ 25/4 = 169/4 – a2

∴ a2 = 169/4 - 25/4

∴ a2 =  144/4 = 36

∴ The required equation of hyperbola is

x^2/36 - y^2/(25/4) = 1,

i.e., x^2/36 - (4y^2)/25 = 1

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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. (22) (i) | Page 178