find the equation of the elipse with the foci (4.0) (-4,0)
It's from James Stewart 9th edition
#I'm trying to find the equation but I think it's incomplete
viral niche
harsh arrowBOT
signal tangle
the focal length is 4
the equation is c^2 = a^2-b^2
so a^2-b^2 = 16
that is not enough information to define an ellipse. I can have a=5 and b=3. I can also have a=6 and b=sqrt(20)
I would need a point or what either a or b is
viral niche
that is not enough information to define an ellipse. I can have a=5 and b=3. I c...
I couldn't solve it in the class also
viral niche
Yes 😔
signal tangle
i guess you could say that b=sqrt(a^2-16)
viral niche
I will ask the prof tomorrow I think it's incomplete
signal tangle
no no, what you do is say a=5 and b=3
if there are multiple possible solutions - even if it looks like they made a mistake - just write down one possible solution
you could also just write down b=sqrt(a^2-16)
and have x^2/a^2 + y^2/(a^2-16) = 1
and say a is any number
well it must be a>4 for it to be an ellipse, otherwise it'd be a hyperbola - but the foci would still be (4,0) and (-4,0)
compact sonnet
Yeah, an eclipse is not defined uniquely by its foci