How do you graph #r(2 + cos theta) = 1#?
↳Redirected from
"What is Arithmetic Mean?"
This is polar equation# (1/2)/r=1+(1/2)cos theta# of an ellipse referred to a focus as pole and major axis (in the direction of nearer end) as initial line. Major axis = 4/3 and eccentricity = 1/2..
Compare with the standard form #l/r=1+e cos theta#, the rearranged equation .# (1/2)/r=1+(1/2)cos theta#
#e=1/2 and l = a (1-e^2)=1/2#.
#a=1/(2(1-1/4))=2/3#.
O(0, 0) is a focus S.
The other focus S'#(2ae, pi) = (2/3, pi)#
The center C is the midpoint #(1/3, pi)#, in-between.
Put #theta =0, pi# in the equation to get ends of the major axis,
#A(1/3, 0), A'(1, pi)#
Put # r = a =2/3# to get the ends of the minor axis, B(2/3, 2pi/3), B'(2/3, -2pi/3)#.
