Problem

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

Solution

Step 1 :\(y^2 + 2y + 1 - 1 + 12x - 35 = 0\)

Step 2 :\((y+1)^2 = 12x - 36\)

Step 3 :\((y+1)^2 = 12 \left(x - 3 \right)\)

Step 4 :\(F_1 = (-3, 1)\)

Step 5 :\(D_1: x = 4 \)

Step 6 :\(V_1 = \left(\frac{1}{2}, 1\right)\)

Step 7 :\(x^2 - 2x + 1 - 1 - 4y + 9 = 0\)

Step 8 :\((x-1)^2 = 4 \left(2y - 5 \right)\)

Step 9 :\(F_2 = \left(\frac{5}{4}, -1\right)\)

Step 10 :\(D_2: y = 3\)

Step 11 :\(V_2 = \left(\frac{5}{4}, \frac{5}{2} \right)\)

From Solvely APP
Source: https://solvelyapp.com/problems/10551/

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