Ano ang vertex, focus at directrix ng 9y = x ^ 2-2x + 9?

Sagot:

Vertex #(1, 8/9)#

Tumuon #(1,113/36)#

Directrix # y = -49 / 36 #

Given -

# 9y = x ^ 2-2x + 9 #

kaitaasan?

Tumuon?

Directrix?

# x ^ 2-2x + 9 = 9y #

Upang makahanap ng Vertex, Focus at directrix, kailangan naming muling isulat ang ibinigay na equation sa vertex form i.e., # (x-h) ^ 2 = 4a (y-k) #

# x ^ 2-2x = 9y-9 #

# x ^ 2-2x + 1 = 9y-9 + 1 #

# (x-1) ^ 2 = 9y-8 #

# (x-1) ^ 2 = 9 (y-8/9) #

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Upang mahanap ang equation sa mga tuntunin ng # y # Ito ay hindi nagtanong sa problema

# 9 (y-8/9) = (x-1) ^ 2 #

# y-8/9 = 1 / 9. (x-1) ^ 2 #

# y = 1 / 9. (x-1) ^ 2 + 8/9 #

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Gumamit tayo # 9 (y-8/9) = (x-1) ^ 2 # upang mahanap ang vertex, focus at directrix.

# (x-1) ^ 2 = 4 xx 9/4 (y-8/9) #

Vertex #(1, 8/9)#

Tumuon #(1,(8/9+9/4))#

Tumuon #(1,113/36)#

Directrix # y = 8 / 9-9 / 4 #

Directrix # y = -49 / 36 #