Respuesta :
Answer:
The equation of the parabola is given as follows;
[tex]\frac{y ^2}{144} - \frac{x ^2}{64} = 1[/tex]
Step-by-step explanation:
Here we have the general equation of a vertical hyperbola, where the y term is positive is given by the relation;
[tex]\frac{(y - k )^2}{b^2} - \frac{(x - h )^2}{a^2} = 1[/tex]
Where:
(h, k) are the coordinates of the center which is given as (0, 0)
a = Horizontal distance from the center of the hyperbola = 8
b = Vertical distance from the center of the hyperbola = 12
Plugging in the values, we have the equation of the parabola given as follows;
[tex]\frac{(y - 0 )^2}{12^2} - \frac{(x - 0 )^2}{8^2} = 1 = \frac{y ^2}{12^2} - \frac{x ^2}{8^2} = 1[/tex]
Hence the equation of the parabola is given as follows;
[tex]\frac{y ^2}{144} - \frac{x ^2}{64} = 1[/tex]
