Complete the square to put the parabola in standard form. Then find the vertex, directrix, focus, and graph the parabola.
1. $y^{2} + 2 y + 12 x - 35 = 0$
Focus
Directrix
Vertex
2. $x^{2} - 2 x - 4 y + 9 = 0$
Focus
Directrix
Vertex

Answer

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Answer

$V_{2} = (\frac{5}{4}, \frac{5}{2})$

Steps

Step 1 ： $y^{2} + 2 y + 1 - 1 + 12 x - 35 = 0$

Step 2 ： $(y + 1)^{2} = 12 x - 36$

Step 3 ： $(y + 1)^{2} = 12 (x - 3)$

Step 4 ： $F_{1} = (- 3, 1)$

Step 5 ： $D_{1} : x = 4$

Step 6 ： $V_{1} = (\frac{1}{2}, 1)$

Step 7 ： $x^{2} - 2 x + 1 - 1 - 4 y + 9 = 0$

Step 8 ： $(x - 1)^{2} = 4 (2 y - 5)$

Step 9 ： $F_{2} = (\frac{5}{4}, - 1)$

Step 10 ： $D_{2} : y = 3$

Step 11 ： $V_{2} = (\frac{5}{4}, \frac{5}{2})$