Hvordan finder du en ækvivalent ligning af x ^ 2 + 4y ^ 2 = 4 i polære koordinater?

Svar:

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

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

Vi bruger de to formler:

# x = rcostheta #

# Y = rsintheta #

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

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

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

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

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

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