תשובה:
# r ^ 2 = 4 (cos ^ 2theta + 4sin ^ 2theta) #
# r = sqrt (4 / cos ^ 2theta + 4sin ^ 2theta)) = 2 / sqrt (cos ^ 2theta + 4sin ^ 2theta) # #
הסבר:
נשתמש בשתי הנוסחאות:
# x = rcostheta #
# y = rsintheta #
# x ^ 2 = r ^ 2cos ^ 2theta #
# y ^ 2 = r ^ 2sin ^ 2theta #
# r ^ 2cos ^ 2theta + 4r ^ 2sin ^ 2theta = 4 #
# r ^ 2 (cos ^ 2theta + 4sin ^ 2theta) = 4 #
# r ^ 2 = 4 (cos ^ 2theta + 4sin ^ 2theta) #
# r = sqrt (4 / cos ^ 2theta + 4sin ^ 2theta)) = 2 / sqrt (cos ^ 2theta + 4sin ^ 2theta) # #
