Ako zistíte ekvivalentnú rovnicu x ^ 2 + 4y ^ 2 = 4 v polárnych súradniciach?

odpoveď:

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

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

Použijeme tieto 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) #