How do you find the coordinates of the vertices, foci, and the equation of the asymptotes for the hyperbola (y−3)225−(x−2)216=1?

1 Answer
Narad T.
Oct 24, 2016

The vertices are (2,8) and (2,−2)
The foci are (2,3+√41) and (2,3−√41)
The equations of the asymptotes are (y=3+54(x−3))
and (3−54(x−3))

Explanation:

Looking at the equation it's an up-down hyperbola

The center of the hyperbola is (2,3)

The vertices are (2,8) and (2,−2)

The slope of the asymptotes ares (54) and (−54)

The equations of the asymptotes are (y=3+54(x−3))
and (3−54(x−3))

To calculate the foci, we need c=±√16+25=√41

The foci are (2,3+√41) and (2,3−√41)

Related questions
See all questions in Standard Form of the Equation
Impact of this question
1971 views around the world
You can reuse this answer
Creative Commons License