# 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

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

#### 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

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. (22) (iii) | Page 178