Kako pronaći ekvivalent jednadžbe x ^ 2 + 4y ^ 2 = 4 u polarnim koordinatama?

Odgovor:

# R ^ 2 = 4 / (cos ^ 2 theta + 4sin ^ 2 theta) #

# R = sqrt (4 / (cos ^ 2 theta + 4sin ^ 2 theta)) = 2 / sqrt (cos ^ 2 theta + 4sin ^ 2 theta) #

Koristit ćemo dvije formule:

# x = rcostheta #

# Y = rsintheta #

# X ^ 2-r ^ 2cos ^ 2 theta #

# Y ^ 2-r ^ 2sin ^ 2 theta #

# ^ R ^ 2 theta 2cos + 4r ^ 2sin ^ 2 theta = 4 #

# R ^ 2 (cos ^ 2 theta + 4sin ^ 2 theta) = 4 #

# R ^ 2 = 4 / (cos ^ 2 theta + 4sin ^ 2 theta) #

# R = sqrt (4 / (cos ^ 2 theta + 4sin ^ 2 theta)) = 2 / sqrt (cos ^ 2 theta + 4sin ^ 2 theta) #