To explain:
a. How to determine the length of the transverse axis by standar
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
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,
, with asymptotes , vertices ,and foci where
The transverse axis is the line segment connecting the vertices of the hyperbola. Here, as the vertices are , 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,
, with asymptotes , vertices , and foci where , 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,
, with asymptotes , and foci where .
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, then the hyperbola is said to have a horizontal transverse axis and if the hyperbola is in the form then the hyperbola is said to have a vertical transverse axis.