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) ‍ .

https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/xff63fac4:hs-geo-parabola/v/equation-for-parabola-from-focus-and-directrix
In this case, the formula becomes entirely different. The process of obtaining the equation is similar, but it is more algebraically intensive. Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y - mx - b)^2 / (m^2 +1) = (x - h)^2 + (y - k)^2. Equivalently, you could put it in general form:

https://www.youtube.com/watch?v=jUJEFAi3mP8
Learn how to find the equation of a parabola given the focus and directrix in this free math video tutorial by Mario's Math Tutoring.0:10 What is a Parabola0

https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-conic-sections/xff63fac4:hs-geo-parabola/e/equation-of-parabola-from-focus-and-directrix
Write the equation for a parabola with a focus at ( 1, 2) and a directrix at y = 6 . y =. Report a problem. 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 anyone, anywhere.

https://www.youtube.com/watch?v=MpWP096ctic
A parabola is the shape of the graph of a quadratic equation. A parabola can... Learn how to write the equation of a parabola given the focus and the directrix.

https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_2e_(OpenStax)/10%3A_Analytic_Geometry/10.04%3A_The_Parabola
HOW TO. Given its focus and directrix, write the equation for a parabola in standard form. Determine whether the axis of symmetry is the x- or y-axis.. If the given coordinates of the focus have the form (p,0),(p,0), then the axis of symmetry is the x-axis.Use the standard form y2=4px.y2=4px.

https://math.libretexts.org/Bookshelves/Algebra/College_Algebra_1e_(OpenStax)/08%3A_Analytic_Geometry/8.04%3A_The_Parabola
A parabola is the set of all points in a plane that are the same distance from a fixed line, called the directrix, and a fixed point (the focus) not on the directrix. The standard form of a parabola with vertex and the x -axis as its axis of symmetry can be used to graph the parabola. If , the parabola opens right.

https://openstax.org/books/college-algebra-2e/pages/8-3-the-parabola
Given its focus and directrix, write the equation for a parabola in standard form. Determine whether the axis of symmetry is the x- or y-axis. If the given coordinates of the focus have the form (p, 0), (p, 0), then the axis of symmetry is the x-axis. Use the standard form y 2 = 4 p x. y 2 = 4 p x.

https://www.symbolab.com/study-guides/collegealgebra1/writing-equations-of-parabolas-in-standard-form.html
How To: Given its focus and directrix, write the equation for a parabola in standard form. Determine whether the axis of symmetry is the x- or y-axis.. If the given coordinates of the focus have the form [latex]\left(p,0\right)[/latex], then the axis of symmetry is the x-axis.Use the standard form [latex]{y}^{2}=4px[/latex].

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.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://study.com/skill/learn/how-to-derive-the-equation-of-a-parabola-given-its-focus-directrix-explanation.html
Step 1: Use the directrix to determine the orientation of the parabola. If the equation of the directrix is of the form y = b, for some number b, then the directrix is horizontal and the parabola

https://www.youtube.com/watch?v=QbR4_BHGpdo
A parabola is defined as the set of all points equidistant from a given focus and directrix. It sounds complicated and overwhelming but it's as simple as usi

https://courses.lumenlearning.com/ivytech-collegealgebra/chapter/writing-equations-of-parabolas-in-standard-form/
How To: Given its focus and directrix, write the equation for a parabola in standard form. Determine whether the axis of symmetry is the x - or y -axis. If the given coordinates of the focus have the form. ( p, 0) \displaystyle \left (p,0\right) (p, 0), then the axis of symmetry is the x -axis. Use the standard form.

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.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://cdn.kutasoftware.com/Worksheets/Alg2/Equations%20of%20Parabolas.pdf
Use the information provided to write the intercept form equation of each parabola. 23) 24) = −( x + 7)( x − 4) = y2 + 20 y + 103. Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com.

https://www.mathway.com/popular-problems/Algebra/918851
Find the Parabola with Focus (1,2) and Directrix y=-2 (1,2) y=-2. Step 1. Since the directrix is vertical, use the equation of a parabola that opens up or down. Step 2. Find the vertex. ... Substitute in the known values for the variables into the equation. Step 5. Simplify. Step 6

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.omnicalculator.com/math/parabola
The standard form of a quadratic equation is y = ax² + bx + c.You can use this vertex calculator to transform that equation into the vertex form, which allows you to find the important points of the parabola - its vertex and focus.. The parabola equation in its vertex form is y = a(x - h)² + k, where:. a — Same as the a coefficient in the standard form;

https://www.purplemath.com/modules/parabola3.htm
For instance, if you are given the vertex (h, k) and the directrix x = a of a parabola, then you can plug this information into the vertex form of the parabola's equation, and that is your answer; nothing more is required. Write an equation for the parabola with focus at (0, −2) and directrix x = 2. The vertex is always halfway between the

https://math.libretexts.org/Courses/Mission_College/MAT_03B_Calculus_II_(Kravets)/07%3A_Parametric_Equations_and_Polar_Coordinates/7.02%3A_Conic_Sections
Identify the equation of a parabola in standard form with given focus and directrix. Identify the equation of an ellipse in standard form with given foci. Identify the equation of a hyperbola in standard form with given foci. Recognize a parabola, ellipse, or hyperbola from its eccentricity value. Write the polar equation of a conic section

https://www.mathway.com/popular-problems/Algebra/719145
Since the directrix is vertical, use the equation of a parabola that opens up or down. Step 2. Find the vertex. Tap for more steps... Step 2.1. The vertex is halfway between the directrix and focus. Find the coordinate of the vertex using the formula. The coordinate will be the same as the coordinate of the focus. Step 2.2. Simplify the vertex.

https://www.numerade.com/ask/question/determine-the-vertex-focus-and-directrix-for-the-parabola-y-frac14x42-the-vertex-is-square-type-an-ordered-pair/
Determine the directrix of the parabola. The directrix is a line that is the same distance from the vertex as the focus but in the opposite direction. Since the focus is 1 unit below the vertex, the directrix is 1 unit above the vertex: \[ \text{Directrix} = y = 0 + 1 = 1 \] So, the directrix is: \[ y = 1 \] Summary: - The vertex is \((-4, 0)\).

https://www.numerade.com/ask/question/show-that-a-conic-with-focus-at-the-origin-eccentricity-e-and-directrix-x-d-has-polar-equation-r-ed-1ecos-theta/
Recall the definition of a conic section in terms of its focus, directrix, and eccentricity. A conic section is defined as the set of all points \( P \) such that the ratio of the distance from \( P \) to the focus (denoted as \( F \)) and the distance from \( P \) to the directrix is equal to the eccentricity \( e \). Step 2/12

https://www.mathway.com/popular-problems/Algebra/736835
Find the Parabola with Focus (2,0) and Directrix x=-2 (2,0) x=-2. Step 1. Since the directrix is horizontal, use the equation of a parabola that opens left or right. Step 2. Find the vertex. ... Substitute in the known values for the variables into the equation. Step 5. Simplify. Step 6