please need help on this problems Find an equation of the parabola with vertex a

Question

please need help on this problems

Find an equation of the parabola with vertex at (-2, 6) and focus at (0, 6). Graph the equation. Analyze the given equation of an Ellipse and graph it.? 8x^2 + 2y^2 - 16x + 8y - 8 = 0 Solve the system of equations using a Matrix Inverse: x - 2y - 4z = 7, 2x - 3y - 6z = 5, -3x + 6y + 15z = 0 And show that the given matrices A and B are inverse to each other. A = [1 2 -3 -2 -3 6 -4 -6 15], B = [-3 -4 1 2 1 0 0 -2/3 1/3] Evaluate the determinant of the matrix. A = [4 0 -2 3 2 -1 -1 5 6] Find t partial fraction decomposition of x^2 + 5/x(x - 1)^3 Find the partial fraction decomposition of x^3 + 2x^2/(x^2 + 4)^2

Explanation / Answer

Vertex ( -2, 6) and focus (0, 6)

Since the xycoordinates of the vertex and focus are the same, they are one of top of the other, so this is a regular horizontal parabola,

4p(x – h)= (y – k)^2

p = 2

8(x+2) = ( y - 6)^2

x +2 = (1/8)( y - 6)^2

x = (1/8)(y - 6)^2 -2

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