If the axis of symmetry is x− axis, then the directrix of the parabola with the focus a, and the vertex (h,k) is, x=h±a. Similarly, for y− axis, the directrix is y=k±a. How does one find the equation of a parabola given the focus and directrix? The equation of a ...
So, the first step in how to find the equation of a parabola is to determine the orientation. For example, ''What is the equation of a parabola with vertex (0, 0) and focus (0, 3)?'' would indicate that the parabola opens up because the focus is above the vertex, while ''What...
The Focal Distance or directrix:The focal distance of any point p(x, y) on the parabola y2= 4ax is the distance between point ‘p’ and focus. Focal distance = x + a Position of a point with respect to parabola For parabola S≡y2−4ax =0, p(x1,y1) S1=y12−4ax1 When, S1...
The latus rectum of aparabolais the chord that is passing through the focus of the parabola and isperpendicularto the axis of the parabola. Thelatus rectum of parabolacan also be understood as the focal chord which is parallel to thedirectrix of parabola. The length of latus rectum for a s...
What is the center of a parabola called? The point which bisects every chord of the conic passing through itis called the Centre of the parabola. i.e. the origin is the vertex of the parabola. The fixed line is known as Directrix. A chord passing through the focus is known as focal ...
For a conic section, the locus of any point on it is such that its ratio of the distance from the fixed point - focus, and its distance from the fixed line - directrix is a constant value is called the eccentricity.Eccentricity: (e < 1). The ratio of the distance of the focus ...
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Notice that the x-coordinate is the same for both the vertex and focus. So, when working with an equation in standard form, the vertex can easily be found once the focus is calculated. Other points can then be used to graph the parabola. For example, look again at the equation {eq}(...