Q. 6 B4.3( 3 Votes )

# Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following cases:

conjugate axis is 5 and the distance between foci = 13

Answer :

**Given:** the distance between the foci = 13 and conjugate axis is 5

**To find:** the equation of the hyperbola

**Formula used:**

For hyperbola:

Distance between the foci is 2ae and b^{2} = a^{2}(e^{2} – 1)

Length of conjugate axis is 2b

Therefore

2ae = 13

b^{2} = a^{2}(e^{2} – 1)

⇒ b^{2} = a^{2}e^{2} – a^{2}

Equation of hyperbola is:

Hence, required equation of hyperbola is **25x ^{2} – 144y^{2} = 900**

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