Question

What is the length of the transverse axis (y-2)^2/16 - (x+1)^2/144= 1

Answer 1

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:$\frac{(y-2)^{2} }{16}$$-\frac{(x+1)^{2} }{144 }$$=1$

Rewrite this equation as $\frac{(y-2)^{2} }{4^{2} }$$-\frac{(x+1)^{2} }{12^{2} }$$=1$

When comparing this equation to the common hyperbola equation with a vertical transverse axis is $\frac{(y-k)^{2} }{a^{2} }$$-\frac{(x+h)^{2} }{b^{2} }$$=1$

$h = -1$

$k= -2$

$a = 4$

$b = 12$

The length of the transverse axis is$2a = 2*4$

                                                               $=8.$

The length of the transverse axis is 8.

To learn more about the length of the transverse axis, refer to:

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