Hoe converteer je 9 = (- 2x + y) ^ 2-5y + 3x naar polaire vorm?

Antwoord:

# 9 = 4r ^ ^ 2 2cos (theta) -4R 2sinthetacostheta ^ + ^ r ^ 2 2sin (theta) -5rsintheta + 3rcostheta = r (sintheta (r (sintheta-4costheta) -5) + costheta (4rcostheta + 3)) #

Uitleg:

# X = rcostheta #

# Y = rsintheta #

# 9 = (- 2 (rcostheta) + rsintheta) ^ 2-5rsintheta + 3rcostheta #

# 9 = 4r ^ ^ 2 2cos (theta) -4R 2sinthetacostheta ^ + ^ r ^ 2 2sin (theta) -5rsintheta + 3rcostheta #

# 9 = r (sintheta (r (sintheta-4costheta) -5) + costheta (4rcostheta + 3)) #