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.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://math.libretexts.org/Bookshelves/Calculus/Calculus_%28OpenStax%29/11%3A_Parametric_Equations_and_Polar_Coordinates/11.05%3A_Conic_Sections
a focus (plural: foci) is a point used to construct and define a conic section; a parabola has one focus; an ellipse and a hyperbola have two eccentricity the eccentricity is defined as the distance from any point on the conic section to its focus divided by the perpendicular distance from that point to the nearest directrix focal parameter

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.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://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/09%3A_Curves_in_the_Plane/9.01%3A_Conic_Sections
Example \(\PageIndex{2}\): Finding the focus and directrix of a parabola. Find the focus and directrix of the parabola \(x=\frac18y^2-y+1\). The point \((7,12)\) lies on the graph of this parabola; verify that it is equidistant from the focus and directrix. Solution. We need to put the equation of the parabola in its general form.

https://www.mathsisfun.com/geometry/conic-sections.html
We can say that any conic section is: "all points whose distance to the focus is equal. to the eccentricity times the distance to the directrix ". For: 0 < eccentricity < 1 we get an ellipse, eccentricity = 1 a parabola, and. eccentricity > 1 a hyperbola. A circle has an eccentricity of zero, so the eccentricity shows us how "un-circular" the

https://www.classcentral.com/course/youtube-finding-the-focus-and-directrix-of-a-parabola-conic-sections-154554
This course teaches how to find the focus and directrix of a parabola in conic sections. The learning outcomes include graphing parabolas in standard form, graphing parabolas with the focus and directrix, identifying the vertex of a parabola, and writing equations in standard form. The teaching method is through a video tutorial.

https://brilliant.org/wiki/conics-parabola-general/
A parabola is a type of conic section, defined as follows: Given a specific point (the focus) and a specific line (the directrix), the parabola is the locus of all points such that its distance from the focus is equal to its perpendicular distance from the directrix, provided the focus doesn't lie on the directrix.

https://www.youtube.com/watch?v=okXVhDMuGFg
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/geometry/xff63fac4:hs-geo-coni

https://en.wikipedia.org/wiki/Conic_section
Conic sections of varying eccentricity sharing a focus point and directrix line, including an ellipse (red, e = 1/2), a parabola (green, e = 1), and a hyperbola (blue, e = 2). The conic of eccentricity 0 in this figure is an infinitesimal circle centered at the focus, and the conic of eccentricity ∞ is an infinitesimally separated pair of lines.

https://mathworld.wolfram.com/ConicSectionDirectrix.html
The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from the focus is proportional to the horizontal distance from the directrix, with r being the constant of proportionality. If the ratio r=1, the conic is a parabola, if r<1, it

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://math.libretexts.org/Bookshelves/Calculus/Map%3A_Calculus__Early_Transcendentals_(Stewart)/10%3A_Parametric_Equations_And_Polar_Coordinates/10.06%3A_Conic_Sections_in_Polar_Coordinates
Identifying a Conic in Polar Form. Any conic may be determined by three characteristics: a single focus, a fixed line called the directrix, and the ratio of the distances of each to a point on the graph.Consider the parabola \(x=2+y^2\) shown in Figure \(\PageIndex{2}\).. Figure \(\PageIndex{2}\) We previously learned how a parabola is defined by the focus (a fixed point) and the directrix (a

https://www.pearson.com/channels/college-algebra/asset/e2492356/conic-sections-parabola-find-the-focus-and-directrix
Conic Sections, Parabola : Find the Focus and Directrix. Skip to main content. College Algebra Start typing, then use the up and down arrows to select an option from the list. ... Conic Sections, Parabola : Find the Focus and Directrix. patrickJMT. 304. views. 05:41. Conic Sections, Parabola: Sketch Graph by Finding Focus, Directrix, Points

https://owlcation.com/stem/How-to-Understand-the-Equation-of-a-Parabola-Directrix-and-Focus
When a plane intersects a cone, we get different shapes or conic sections where the plane intersects the outer surface of the cone. If the plane is parallel to the bottom of the cone, we just get a circle. As the angle A in the animation below changes, it eventually becomes equal to B, and the conic section is a parabola.

https://quizlet.com/715181899/conic-sections-parabola-flash-cards/
This equation is a parabola whose vertex is at (2, 3), opens down, and p = 4. -16 (y + 3 )= (x+2) This equation is a parabola whose vertex is at (4, 3), opens down, and focus at (4, -3) -24 (y - 3 )= (x-4)^2. Study with Quizlet and memorize flashcards containing terms like 16x = y^2 The directrix of the parabola is:, -8x=y^2 The focus of the

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://math.stackexchange.com/questions/2421094/find-focus-directrix-and-graph-of-a-parabola
Find vertex focus and directrix of parabola. 9x2 + 16y2 − 24xy − 18x − 101y + 109 = 0. 9 x 2 + 16 y 2 − 24 x y − 18 x − 101 y + 109 = 0. Then sketch the graph. My work. 3x − 4Y2 = 18x + 101y − 109 3 x − 4 Y 2 = 18 x + 101 y − 109. Here Y = 3x − 4y Y = 3 x − 4 y and X = 18x + 101y − 109 X = 18 x + 101 y − 109 then I

https://www.pearson.com/channels/precalculus/asset/ea9cb371/conic-sections-parabola-find-the-focus-and-directrix
Conic Sections, Parabola : Find the Focus and Directrix. Skip to main content. Precalculus Start typing, then use the up and down arrows to select an option from the list. ... Conic Sections, Parabola : Find the Focus and Directrix. patrickJMT. 216. views. 05:41. Conic Sections, Parabola: Sketch Graph by Finding Focus, Directrix, Points

https://math.stackexchange.com/questions/2157306/find-vertex-when-focus-and-directrix-of-parabola-is-given
Focus is $(1,1)$ and equation to the Directrix is $3x+4y-2=0$ I've successfully derived the equation of Parabola in second degree general form which is: $16x^2 - 38x+9y^2 - 34y+46-24xy=0$ Also, find the equation of its axis.

https://math.stackexchange.com/questions/2173548/why-does-the-directrix-of-a-conic-section-have-that-name
Conic sections may be defined in terms of the "focus-directrix property", as the loci of points that satisfy a particular relationship involving a point called the focus and a line called the directrix. While the name "focus" for the point seems easily explicable, the name "directrix" for the line is less so (to me).