Q. 11 F5.0( 1 Vote )

# In each of the following find the equations of the hyperbola satisfying the given conditionsfoci , the latus-rectum = 8

Given: Foci and the latus-rectum = 8

To find: equation of the hyperbola

Formula used:

The standard form of the equation of the hyperbola is,

Coordinates of the foci for a standard hyperbola is given by (±ae, 0)

Length of latus rectum is

According to the question:

We know,

b2 = a2(e2 – 1)

4a = 45 – a2

a2 + 4a – 45 = 0

a2 + 9a – 5a – 45 = 0

a(a + 9) – 5(a + 9) = 0

(a + 9)(a – 5) = 0

a = -9 or a = 5

Since a is a distance, and it can’t be negative

a = 5

a2 = 25

b2 = 4a

b2 = 4(5)

b2 = 20

Hence, equation of hyperbola is:

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