To explain: a. How to determine the length of the transverse axis by standar

Tyra

Tyra

Answered question

2021-09-12

To explain:
a. How to determine the length of the transverse axis by standard equation of a hyperbola.
b. How to determine whether the transverse axis is vertical or horizontal

Answer & Explanation

Mayme

Mayme

Skilled2021-09-13Added 103 answers

Given:
The standard equation of a hyperbola.
Calculation:
a. Let us consider the standard equation of the hyperbola passing through the origin (0,0) to be of the form,
x2a2y2b2=1, with asymptotes y=±bax, vertices (±a,0),and foci (±c,0) where c=a2+b2
The transverse axis is the line segment connecting the vertices of the hyperbola. Here, as the vertices are (±a,0), therefore the length of the transverse axis is 2a
b. If the standard equation of the hyperbola passing through the origin (0,0) to be of the form,
x2a2y2b2=1, with asymptotes y=±bax, vertices (±a,0), and foci (±c,0) where c=a2+b2, Then the hyperbola is said to have a horizontal transverse axis. And, If the standard equation of the hyperbola passing through the origin (0,0) to be of the form,
y2a2x2b2=1, with asymptotes y=±abx, and foci (0,±c) where c=a2+b2.
Then the hyperbola is said to have a vertical transverse axis.
Conclusion:
a. Length of the transverse axis is 2a
b. If the hyperbola is in the form, x2a2y2b2=1 then the hyperbola is said to have a horizontal transverse axis and if the hyperbola is in the form y2a2x2b2=1 then the hyperbola is said to have a vertical transverse axis.

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