kmp44 Posts: 1, Reputation: 1 New Member #1 Dec 16, 2009, 10:58 AM
write the equation 0f the hyperbola
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
 galactus Posts: 2,271, Reputation: 282 Ultra Member #2 Dec 16, 2009, 03:32 PM
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 $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$

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