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Determine the equation of the hyperbola which satisfies the given conditions: Foci (0, ±13), the conjugate axis is of length 24.

Determine the equation of the hyperbola which satisfies the given conditions: Foci (0, ±13), the conjugate axis is of length 24.

Grade:12th pass

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
2 years ago
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Given that: Foci (0, ±13), Conjugate axis length = 24

It is noted that the foci are on the y-axis.

Therefore, the equation of the hyperbola is of the form:

(y^2/a^2)-(x^2/b^2) = 1 …(1)

Since the foci are (0, ±13), we can get

C = 13

It is given that, the length of the conjugate axis is 24,

It becomes 2b = 24

b= 24/2

b= 12

And, we know that a^2+ b^2= c2

To find a, substitute the value of b and c in the above equation:

a^2+ 122= 132

a^2= 169-144

a^2= 25

Now, substitute the value of a and b in equation (1), we get

(y^2/25)-(x^2/144) = 1, which is the required equation of the hyperbola.

Thanks

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