Paano mo i-convert ang y = -y ^ 2-3x ^ 2-xy sa isang polar equation?

Sagot:

#r = - (sintheta) / (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) #

Paliwanag:

Isulat muli bilang:

# y ^ 2 + 3x ^ 2 + xy = -y #

Kapalit sa:

# x = rcostheta #

# y = rsintheta #

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

# r ^ 2 (sintheta) ^ 2 + 3r ^ 2 (costheta) ^ 2 + r ^ 2 (costhetasintheta) = - rsintheta #

Hatiin ang magkabilang panig ng # r #

#r (sintheta) ^ 2 + 3r (costheta) ^ 2 + r (costhetasintheta) = - sintheta #

I-Factorise out # r #:

#r (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) = - sintheta #

Gumawa # r # ang paksa:

#r = - (sintheta) / (sin ^ 2theta + 3cos ^ 2theta + costhetasintheta) #