Question 1047761: sketch the hyperbola and label the vertices,foci,and asymptot of x²/16-y²/4=1
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! Need to Know:
Standard Form of an Equation of an Hyperbola opening right and left is:
 with C(h,k) and vertices 'a' units right and left of center, 2a the length of the transverse axis. e = c/a.
Foci are  = c- units right and left of center along y = k & Asymptotes Lines passing thru C(h,k), with slopes m = ± b/a
__________________________________________________________________________________
x²/16-y²/4=1
C(0,0)
vertices 'a' units right and left of center C(0,0)
V(4,0) and V(-4, 0)
|
Foci are  = c- units right and left of center C(0,0) along y = k
c = 2√5
F( 2√5, 0) and F(-2√5, 0)
|
Asymptotes Lines passing thru C(0,0), with slopes m = ± b/a
m = ± 2/4 =± 1/2
y = ±(1/2)x
Sketch in the Hyperbola opening right and left
|
|
|
