A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola and the lotus rectum. Equation of a parabola given the vertex and focus is: ([I]x[/I] – [I]h[/I])^2 = 4[I]p[/I]([I]y[/I] – [I]k[/I]) The vertex (h, k) is 4, -2 The distance is p, and since the y coordinates of -2 are equal, the distance is 6 - 4 = 2. So p = 2 Our parabola equation becomes: (x - 4)^2 = 4(2)(y - -2) [B](x - 4)^2 = 8(y + 2)[/B] Latus rectum of a parabola is 4p, where p is the distance between the vertex and the focus LR = 4p LR = 4(2) [B]LR = 8[/B]

if the vertex of a parabola is (4,9) what is the axis of symmetry [B]x = 4[/B]

Free Polygons Calculator - Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon. This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax² + bx + c = 0. Also generates practice problems as well as hints for each problem.
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