Question
the vertices are at (2,1) and (2,7) and focus is at (2,*)
write the equation of the hyperbola that meets each set of conditions.
Is the asterisk supposed to be an 8? It has to be some number. I will set this up for you later of you respond. The fomulas you need are in most calculus and analytic geometry texts.
yeah it is an 8
your vertices are (2,1) and (2,7), so your centre is (2,4), the midpoint.
Since your hyperbola is vertical it must have equation:
(x-2)^2 over a^2 - (y-4)^2 over b^2 = -1
the distance from (2,4) to (2,7) is 3, so b=3
the distance from (2,4) to your focus (2,8) is 4, so c=4
recall that in a hyperbola a^2 + b^2 = c^2, substitute to get a^2 = 7
Therefore (x-2)^2 over 7 - (y-4)^2 over 9 = -1
Nice job, reiny! Thanks for helping us out here.
write the equation of the hyperbola that meets each set of conditions.
Is the asterisk supposed to be an 8? It has to be some number. I will set this up for you later of you respond. The fomulas you need are in most calculus and analytic geometry texts.
yeah it is an 8
your vertices are (2,1) and (2,7), so your centre is (2,4), the midpoint.
Since your hyperbola is vertical it must have equation:
(x-2)^2 over a^2 - (y-4)^2 over b^2 = -1
the distance from (2,4) to (2,7) is 3, so b=3
the distance from (2,4) to your focus (2,8) is 4, so c=4
recall that in a hyperbola a^2 + b^2 = c^2, substitute to get a^2 = 7
Therefore (x-2)^2 over 7 - (y-4)^2 over 9 = -1
Nice job, reiny! Thanks for helping us out here.