The parabola, x2 = 8y is shifted to the right by 1 unit and shifted downward by 7units. Find an equation for the shifted parabola and find the new vertex, focus, anddirectrix

Write the equation in vertex form for the parabola with focus (0,–7) and directrix y=3.Simplify any fractions.

Find the focus and directrix of the parabola with the equation x^2 = 8y.Determine the focus and directrix of the parabola given by y^2 = -4x.Find the focus and directrix of the parabola described by the equation y^2 = 6x.Calculate the focus and directrix for the parabola represented by x^2 = -10y.Identify the focus and directrix of the parabola y^2 = 2x + 4.Determine the focus and directrix of the parabola x^2 = 16y + 32.Find the focus and directrix of the parabola y^2 = -3x - 6.Calculate the focus and directrix for the parabola described by x^2 = 12y - 24.Given the focus at F(2, 3) and the directrix y = 1, find the equation of the parabola in standard form.The focus of a parabola is at F(0, -5), and the directrix is the line y = -1. Determine the equation of the parabola in standard form.Find the focus and directrix for the parabola with its vertex at V(3, 4) and opening horizontally.A parabola has a focus at F(1, 2) and an axis of symmetry along the line x = 1. Determine the equation of the parabola in standard form.Given that the vertex of a parabola is at V(-2, 1) and its focus is at F(1, 1), calculate the equation of the parabola in standard form.Find the focus and directrix for the parabola with its vertex at V(0, -3) and opening vertically.Determine the equation of a parabola in standard form with a focus at F(4, 2) and a directrix y = -2.Given that the vertex of a parabola is at V(1, 4) and it opens upward, find the focus and directrix.Convert the equation y = 4x^2 - 8x + 5 into standard form (ax^2 + bx + c = 0), and then find the focus, directrix, and endpoints of the latus rectum.Given the equation 3x^2 + 12x - 4y + 1 = 0, find the standard form of the parabola. Afterward, determine the focus, directrix, and axis of symmetry.Find the standard form of the parabola with a focus at (3, -2) and a directrix at y = -6. Also, find the endpoints of the latus rectum.Convert the equation 2y = x^2 - 6x + 9 into standard form, and then identify the focus, directrix, and axis of symmetry.Given the equation, 4x^2 + 16x - y - 3 = 0, rewrite it in standard form and calculate the focus, directrix, and endpoints of the latus rectum.Find the standard form of the parabola with a focus at (-1, 2) and a directrix at y = -4. Determine the axis of symmetry and the endpoints of the latus rectum.These questions cover different forms and orientations of parabolas and sh

A parabola has the origin as its focus and the line x=2 as the directrix. Then the vertex of the parabola is at

find the vertex , axis , focus , directrix , latus rectum of the parabola 4y

Find the focus of the parabola defined by the equation left bracket, x, minus, 2, right bracket, squared, equals, minus, 32, left bracket, y, plus, 6, right bracket(x−2) 2 =−32(y+6).