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