2
Question
Find the equation of the hyperbola satisfying the give conditions: Foci (0,±13) the conjugate axis is of length 24
Open in App
Solution
It is given that, foci (0,±13), the conjugate axis is of length 24
Here the foci are on the y-axis.
Therefore, the equation of the hyperbola is of the form y2a2−x2b2=1
Since the foci are (0,±13)⇒ae=c=13
Since the length of the conjugate axis is 24,⇒2b=24⇒b=12
We know that a2+b2=c2
∴a2+122=132
⇒a2=169−144=25
Thus the equation of the hyperbola is y225−x2144=1
Here the foci are on the y-axis.
Therefore, the equation of the hyperbola is of the form y2a2−x2b2=1
Since the foci are (0,±13)⇒ae=c=13
Since the length of the conjugate axis is 24,⇒2b=24⇒b=12
We know that a2+b2=c2
∴a2+122=132
⇒a2=169−144=25
Thus the equation of the hyperbola is y225−x2144=1
Suggest Corrections
0
Similar questions