Question

1. Rewrite the given equation in standard from, and then determine the vertex (V), focus (F), and directrix (d) of the parabola. a. b. x==y2 36 c. y2 - 6y + 12x - 3 = 0

Answer 1

0 a y = 1/2 multiply by 4 in both side ty = 4 x 4 x ² 212 ty Standard form of parabola 2 aplyk) t(0-0) ... (2-0) comporing, on Ả= 0, k = 0, tp = 4 vertex = ( thek) > frentex = 10,0) focus= (h, k+P) - 10,0+1) focus = 6011) Directrix » y = k-p y = 0-1 1y = -1 Auswer

5 -) 2-3 y? y² = 36x writing in standard form ( J-) 367-0) comparing with (9-x) = 4p(x-th) .: K=0, h=0, 4p=36 » [P=9 ) Veotex = ( thek) I verter = (0,0)7 focus= (htp, k) (0 +9,0) focus = 19,0) Directrix is x = hp y =o-9 x=9 Answer y2 by +12x-3=0 y2-6 y = -12x +3 y²+ (3) ² - 2xy X3 -12x +3+(3) for completing (9-3)? (square, adding (3)? (y - 3)² = -12 x + 12 - 2x + 379 in both sides

(9-3)?-. -12(x-1) (standared form) comparing with 1-+)? 48 (3-4) now h = 1, K = 3, 4p = -12 » (P=-37 now, vertex = 1 the k) = (1,3) vertex = (1,3) fours [ht pek) - (1 +1-3), 3) (-2,3) fous Directex is x =hop x = 1- (-3) x=4