https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/xff63fac4:hs-geo-parabola/a/parabola-focus-directrix-review
Given the focus and the directrix of a parabola, we can find the parabola's equation. Consider, for example, the parabola whose focus is at ( − 2, 5) and directrix is y = 3 . We start by assuming a general point on the parabola ( x, y) . Using the distance formula, we find that the distance between ( x, y) and the focus ( − 2, 5) is ( x + 2

https://www.effortlessmath.com/math-topics/how-to-find-the-focus-vertex-and-directrix-of-a-parabola/
The vertex of a parabola is the maximum or minimum of the parabola and the focus of a parabola is a fixed point that lies inside the parabola. The directrix is outside of the parabola and parallel to the axis of the parabola. Related Topic. How to Write the Equation of Parabola; Step-by-Step Guide to Finding the Focus, Vertex, and Directrix of

https://www.cuemath.com/geometry/directrix-of-parabola/
The directrix of parabola is x + 5 = 0. The focus of the parabola is (a, 0) = (5, 0). For the parabola having the x-axis as the axis and the origin as the vertex, the equation of the parabola is y 2 = 4ax. Hence the equation of the parabola is y 2 = 4 (5)x, or y 2 = 20x. Therefore, the equation of the parabola is y 2 = 20x.

https://www.mathwarehouse.com/quadratic/parabola/focus-and-directrix-of-parabola.php
The red point in the pictures below is the focus of the parabola and the red line is the directrix. As you can see from the diagrams, when the focus is above the directrix Example 1, the parabola opens upwards. In the next section, we will explain how the focus and directrix relate to the actual parabola. Explore this more with our interactive

https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/xff63fac4:hs-geo-parabola/v/focus-and-directrix-introduction
The first instance is the best. If you have the parabola written out as an equation in the form y = 1/ (2 [b-k]) (x-a)^2 + .5 (b+k) then (a,b) is the focus and y = k is the directrix. This is for parabolas that open up or down, or vertical parabolas. For those that open left or right it is diffeent.

https://www.wikihow.com/Find-Focus-of-Parabola
1. Put the equation into the vertex form of a parabola. Because the portion of the equation is squared, the correct vertex form is , meaning this is a "regular" parabola (it opens either up or down). →. Also note that, because is positive, the parabola opens upward. 2.

https://study.com/skill/learn/how-to-find-the-focus-directrix-of-a-parabola-explanation.html
Find the coordinates of the focus and the equation of the directrix for the parabola given by the equation {eq}{(x-4)}^2=-8(y+1) {/eq}. Step 1: Identify the given equation and determine

https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/xff63fac4:hs-geo-parabola/v/equation-for-parabola-from-focus-and-directrix
- [Voiceover] What I have attempted to draw here in yellow is a parabola, and as we've already seen in previous videos, a parabola can be defined as the set of all points that are equidistant to a point and a line, and the point is called the focus of the parabola, and the line is called the directrix of the parabola.

https://www.mathsisfun.com/geometry/parabola.html
Equations. The simplest equation for a parabola is y = x2. Turned on its side it becomes y2 = x. (or y = √x for just the top half) A little more generally: y 2 = 4ax. where a is the distance from the origin to the focus (and also from the origin to directrix) Example: Find the focus for the equation y 2 =5x.

https://www.cuemath.com/geometry/focus-of-parabola/
Solution: The given focus of the parabola is (a, 0) = (4, 0)., and a = 4. For the parabola having the x-axis as the axis and the origin as the vertex, the equation of the parabola is y 2 = 4ax. Hence the equation of the parabola is y 2 = 4 (4)x, or y 2 = 16x. Therefore, the equation of the parabola is y 2 = 16x.

https://www.varsitytutors.com/hotmath/hotmath_help/topics/focus-of-a-parabola
The focus lies on the axis of symmetry of the parabola. Finding the focus of a parabola given its equation. If you have the equation of a parabola in vertex form y = a ( x − h ) 2 + k , then the vertex is at ( h, k ) and the focus is ( h, k + 1 4 a ) . Notice that here we are working with a parabola with a vertical axis of symmetry, so the x

https://www.youtube.com/watch?v=KYgmOTLbuqE
This video tutorial provides a basic introduction into parabolas and conic sections. It explains how to graph parabolas in standard form and how to graph pa

https://www.youtube.com/watch?v=Ko-CqpNEUWg
Learn how to graph a parabola in standard form when the vertex is not at the origin. We will learn how to graph parabola's with horizontal and vertical open

https://study.com/academy/lesson/the-focus-and-directrix-of-a-parabola.html
It is the graph of a quadratic equation y = a x 2 + b x + c. A parabola can face upwards or downards. The point that is the maximum of a downward facing parabola or the minimum of an upward facing

https://www.khanacademy.org/math/math2/xe2ae2386aa2e13d6:conics/xe2ae2386aa2e13d6:focus-directrix/v/finding-focus-and-directrix-from-vertex
Let's say that the directrix is line y = t. The distance of the x coordinate of the point on the parabola to the focus is (x - a). The distance of the y coordinate of the point on the parabola to the focus is (y - b). Remember the pythagorean theorem. a^2 + b^2 = c^2. We know the a^2 and the b^2.

https://study.com/learn/lesson/parabola-focus-directix-formula-examples.html
The following are the steps to find equation of parabola given focus and directrix: 1. With the given focus and directrix, the distance between the focus and the point on the parabola and the

https://www.omnicalculator.com/math/parabola
Find the coordinates of the focus of the parabola. The x-coordinate of the focus is the same as the vertex's (x₀ = -0.75), and the y-coordinate is: y₀ = c - (b² - 1)/(4a) = -4 - (9-1)/8 = -5. Find the directrix of the parabola. You can either use the parabola calculator to do it for you, or you can use the equation:

https://www.intmath.com/functions-and-graphs/what-is-a-directrix-of-a-parabola.php
The directrix of a parabola is an imaginary straight line perpendicular to the axis that passes through the focus of the parabola. The equation for this line is y=d, where d is equal to the distance between the focus and directrix. This means that when we look at any given point on the parabola, it must be exactly d units away from the directrix.

https://owlcation.com/stem/How-to-Understand-the-Equation-of-a-Parabola-Directrix-and-Focus
One way we can define a parabola is that it is the locus of points that are equidistant from both a line called the directrix and a point called the focus. So, each point P on the parabola is the same distance from the focus as it is from the directrix, as you can see in the animation below.

https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/xff63fac4:hs-geo-parabola/e/equation-of-parabola-from-focus-and-directrix
You might need: Calculator. Write the equation for a parabola with a focus at ( 1, 2) and a directrix at y = 6 . y =. Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for

https://www.varsitytutors.com/hotmath/hotmath_help/topics/finding-the-equation-of-a-parabola-given-focus-and-directrix
Any point, ( x 0 , y 0 ) on the parabola satisfies the definition of parabola, so there are two distances to calculate: Distance between the point on the parabola to the focus Distance between the point on the parabola to the directrix To find the equation of the parabola, equate these two expressions and solve for y 0 .

https://www.geeksforgeeks.org/focus-and-directrix-of-a-parabola/
Using the equation (1), we get. x = x = y 2 = 4ax. It is the standard equation of the parabola. Note: The parabola has two real foci situated on its axis one of which is the focus S and the other lies at infinity.The corresponding directrix is also at infinity. Tracing of the parabola y 2 = 4ax, a>0. The given equation can be written as y = ± 2, we observe the following points from the equation:

https://study.com/skill/learn/how-to-find-the-focus-directrix-of-a-parabola-in-vertex-form-explanation.html
Find the focus and directrix of the parabola y = 1 4 ( x − 3) 2 + 1 . Step 1: Identify h, k, and a for the parabola in vertex form y = a ( x − h) 2 + k by comparison of the constants. From the