Maharashtra State BoardHSC Science (Electronics) 11th
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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

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

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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
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