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The length of the transverse axis is 8.
What is transverse axis length?
- The transverse axis of the hyperbola is the straight line connecting vertices A and A'. The line segment connecting the vertices of a hyperbola is referred to as the transverse axis or AA'.
- The hyperbola's equation is expressed as (yk)2b2(xh)2a2=1). The center is (h,k), b defines the transverse axis, and a defines the conjugate axis. The section of a line where a hyperbola's vertices form.
Given the equation of hyperbola:[tex]\frac{(y-2)^{2} }{16}[/tex][tex]-\frac{(x+1)^{2} }{144 }[/tex][tex]=1[/tex]
Rewrite this equation as [tex]\frac{(y-2)^{2} }{4^{2} }[/tex][tex]-\frac{(x+1)^{2} }{12^{2} }[/tex][tex]=1[/tex]
When comparing this equation to the common hyperbola equation with a vertical transverse axis is [tex]\frac{(y-k)^{2} }{a^{2} }[/tex][tex]-\frac{(x+h)^{2} }{b^{2} }[/tex][tex]=1[/tex]
[tex]h = -1[/tex]
[tex]k= -2[/tex]
[tex]a = 4[/tex]
[tex]b = 12[/tex]
The length of the transverse axis is[tex]2a = 2*4[/tex]
[tex]=8.[/tex]
The length of the transverse axis is 8.
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