I need the conic and locus definition of a hyperbola and the conic definition of a parabola. All the definitions or part of one is asked for.
Thank you so much!
Thank you so much!
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All right. I haven't done this since Algebra and Pre-Calc, so I hope I remembered right.
So for a hyperbola, I believe it is
(x-h)^2 - (y-k)^2 = 1
/a^2........./b^2
(Ignore ...... It is to fill space)
This is where h,k is center.
The (x-h) term would be positive if horizontally major. (open sideways)
The (y-k) term would be positive if vertically major (up and down)
Locus, I think you mean focus?
So take the square root of a^2 + b^2.
Then add that to (h,k)
but it depends on the orientation, so you add it to h or k depending on if it is major one way or the other.
Parabola was
y=a(x-h)^2+k
Where h,k is vertex.
You also have x=a(y-k)^2 + h
if you want it sideways.
To find the focus or directrix of a parabola:
Take the absolute value of 1/(4a).
Then add that to (h,k)
and again it depends if concave up or down
or if sideways.
So for a hyperbola, I believe it is
(x-h)^2 - (y-k)^2 = 1
/a^2........./b^2
(Ignore ...... It is to fill space)
This is where h,k is center.
The (x-h) term would be positive if horizontally major. (open sideways)
The (y-k) term would be positive if vertically major (up and down)
Locus, I think you mean focus?
So take the square root of a^2 + b^2.
Then add that to (h,k)
but it depends on the orientation, so you add it to h or k depending on if it is major one way or the other.
Parabola was
y=a(x-h)^2+k
Where h,k is vertex.
You also have x=a(y-k)^2 + h
if you want it sideways.
To find the focus or directrix of a parabola:
Take the absolute value of 1/(4a).
Then add that to (h,k)
and again it depends if concave up or down
or if sideways.