Jak najdete ekvivalentní rovnici x ^ 2 + 4y ^ 2 = 4 v polárních souřadnicích?

Odpovědět:

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

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

Použijeme tyto dva vzorce:

# 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) #