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x2/242-y2/62=1

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Q: What is the equation for a hyperbola that has a transverse axis length of 24 and is centered at the origin?
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What is the equation of a hyperbola that has a transverse axis of length 24 and is centered at the origin?

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What is the equation for a hyperbola with transverse axis of length 24 and centered at the origin?

The standard form of the equation of a hyperbola with center at the origin isx2/a2 - y2/b2 = 1 where the transverse axis lies on the x-axis,ory2/a2 - x2/b2 = 1 where the transverse axis lies on the y-axis.The vertices are a units from the center and the foci are c units from the center.For both equations, b2 = c2 - a2. Equivalently, c2 = a2 + b2.Since we know the length of the transverse axis (the distance between the vertices), we can find the value of a (because the center, the origin, lies midway between the vertices and foci).Suppose that the transverse axis of our hyperbola lies on the x-axis.Then, |a| = 24/2 = 12So the equation becomes x2/144 - y2/b2 = 1.To find b we need to know what c is.