WebFind the equation of the parabola if the vertex is (1, 4) and the focus is (-2, 4). Solution : From the given information the parabola is symmetric about x -axis and it opens to the left. Distance between vertex and focus = a a = VF = √ [ (1 + 2)2 + (4 - 4)2] = √ (32 + 0) = √9 a = 3 Equation of the parabola : (y - k)2 = -4a (x - h) WebJan 29, 2024 · You are right - since the vertex is above the focus, the parabola must open downwards. So p = − 10 and the parabola has equation ( x − 1) 2 = − 40 ( y − 2). Note that the right hand side is never negative because for all points on the parabola y ≤ 2 (because the parabola opens downwards).

Get the parabola with vertex and focus - WolframAlpha

WebThe vertex is the midpoint between the directrix and focus, which is (2,2) (2,2). Thus we can consider the parabola y^2=4ax y2 = 4ax having been translated 2 units to the right and 2 units upward. Since the distance … WebMay 1, 2024 · The key features of a parabola are its vertex, axis of symmetry, focus, directrix, and latus rectum (Figure 12.3.5 ). When given a standard equation for a parabola centered at the origin, we can easily identify the key features to graph the parabola. A line is said to be tangent to a curve if it intersects the curve at exactly one point. how much is dishnet

Parabolas, Ellipses, and Hyperbolas Calculus II - Lumen Learning

WebCalculus questions and answers. Witing an equation of a parabola given the vertex and the focus Find an equation of the parabola with vertex (-2,-2) and focus (-2,-5). WebNov 10, 2015 · First let the focus F = (a,b) and the directrix is a linear equation y = mx + c We need to find the point P (p, mp + c) on the directrix such that the segment between it. … WebOct 6, 2024 · The equation of the parabola is often given in a number of different forms. One of the simplest of these forms is: (x − h)2 = 4p(y − k) A parabola is defined as the locus (or collection) of points equidistant from … how much is dish worth