Ask Me Help Desk - Write the equation 0f the hyperbola

Quote:

Originally Posted by kmp44

from data the average x-intercept of the path along which the sonic boom can be heard is -8 miles and the average focas is -12 miles,describe the hyperbola

A hyperbola, like an ellipse, has an a and b value corresponding to the semi-major and semi-minor axes.

Center the hyperbola at the origin and it's focal axis is parallel to the x-axis.

We can find b by using $b=\sqrt{c^{2}-a^{2}}$

c is the distance of the foci from the origin and a is the distance of the vertex from the origin. These are given. Use those to find b.

Then, plug those values into the equation of a hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$