Question

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


ρσiทτs кαє внυкσ jisкσ αทsωєr ทαнi ααατα vσ αทsωєr мατ ∂єทα ƒrєє ρσiทτs кαє ℓiyє ρℓʑ!



⚠ѕραммєяѕ ѕταγ αωαγ⚠​​

Answer 1

Answer:

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:

(y2/a2)-(x2/b2) = 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 a2 + b2 = c2

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

a2 + 122 = 132

a2 = 169-144

a2 = 25

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

(y2/25)-(x2/144) = 1, which is the required equation of the hyperbola.

Step-by-step explanation:

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Answer 2

It is given that, foci (±5,0), the transverse axis is of length 8

Here the foci are on the x-axis.

Therefore, the equation of the hyperbola is of the form a2x2−b2y2=1

Since the foci are (±5,0)⇒ae=c=5

Since the length of the transverse axis is 8, ⇒2a=8⇒a=4

We know that a2+b2=c2

42+b2=52

⇒b2=25−16=9

Thus the equation of the hyperbola is 16x2−9y2=1

Step-by-step explanation:

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