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Answer the following: Find the equation of the hyperbola in the standard form if length of the conjugate axis is 3 and distance between the foci is 5 - Mathematics and Statistics

Sum

Answer the following:

Find the equation of the hyperbola in the standard form if length of the conjugate axis is 3 and distance between the foci is 5

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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 = 3

∴ 2b = 3

∴ b = `3/2`

∴ b2 = `9/4`

Distance between foci = 2ae

Given, distance between foci = 5

∴ 2ae = 5

∴ ae = `5/2`

∴ a2e2 = `25/4`

Now, b2 = a2(e2 – 1)

∴ b2 = a2e2 – a2

∴ `9/4 = 25/4` – a2

∴ a2 = `25/4 - 9/4`

∴ a2 = `16/4` = 4

∴ The required equation of hyperbola is

`x^2/4 - y^2/((9/4))` = 1.

i.e., `x^2/4 - (4y^2)/9` = 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) (iii) | Page 178
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