Kako pretvoriti 9 = (- 2x + y) ^ 2-5y + 3x u polarni oblik?

Odgovor:

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

Obrazloženje:

# x = rcostheta #

# Y = rsintheta #

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

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

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