Learn how to find the equation of a parabola with its focus and directrix in this bite-sized video lesson. Enhance your geometry skills by taking a quiz for practice.
Focus: The point (a, 0) is the focus of the parabola Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola. Focal Chord: The focal chord of a parabola is...
Vertex, Focus, and Directrix of a Parabola Important components of a parabola include the vertex, focus, axis of symmetry, latus rectum, and directrix. See Figure 1 for a diagram of these traits. The,, of adescribes how much the shape differs from a circle. The eccentricity of a parabola...
Focus: (14, 0); Directrix: x = -14 Equation of a Parabola: The equation of a parabola centered at the origin and opening to the right is: {eq}\displaystyle x = \frac{1}{4p}y^2 {/eq} where {eq}p = \displaystyle \frac{1}{4a} {/eq}...
Equation of Parabola: In mathematics, a parabola is a type of conic section. It is the locus of points whose distances from a fixed point, called the focus, are equal to the distance from the fixed-line, called the directrix, of the parabola. The stand...
In mathematics, a hyperbola is an important conic section formed by the intersection of the double cone by a plane surface, but not necessarily at the center. A hyperbola is symmetric along the conjugate axis, and shares many similarities with the ellipse. Concepts like foci, directrix, latus ...
The distance from the focus (2, 1) to the directrix x=-4 is 2-(-4)=6, so the distance from the focus to the vertex is 12(6)=3 and the vertex is (-1, 1). Since the focus is to the right of the vertex, p=3. An equation is (y-1)^2=4⋅ 3[x-(-1)], or (y-...
Julie, we can tell this parabola is going to be sideways, given that our vertex is horizontal. Since the directrix is to the left of our focus (which the latus rectum runs through), we know that it's opening to the right and p is going to be positive. ...
To solve the problem, we need to find the equation of the parabola given its vertex and directrix, and then determine the values of
Focus and Directrix Distance formulais used to prove that the distance from the focus to any point in that parabola is equal to the distance from any point of the parabola to the directrix. The formula is: D=(x2−x1)2+(y2−y1)2 ...