With the given focus and directrix, determine the vertex of the parabola. Substitute the obtained vertex in the vector form of parabola. Again, with the values of {eq}a {/eq}, the quadratic equation is obtained. How does one find the focus and directrix? In vertex form if, {eq}(x -...
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Parabolais a quadratic equation that has a curve that opens up or down that represents a function in the form off(x)=ax2+bx+cwhere a, b, and c are constants that will shape the parabola. The major parts of the parabola are thefocus,vertex, and thedirectrix. The parabola comprises equ...
Focus of a Parabola:In mathematics, the focus of a parabola is a point that can be used, along with a line called the directrix, to define the parabola. That is, a parabola is a set of points, such that each point on the parabola is the same distance from the focus of the ...
The length of the latus rectum of a parabola is given by 4a. Since we have a=4:Length of latus rectum=4×4=16 Summary of Results- Vertex: (0,0)- Focus: (0,−4)- Directrix: y=4- Axis: x=0 (y-axis)- Tangent at the vertex: y=0 (x-axis)- Length of latus rectum: 16 ...
Find the vertex, focus, and directrix of the parabola and sketch its graph. 3x2+8y=0 Vertex Form of a Parabola: By now we are quite used to seeing the standard form for a parabola as y(x)=ax2+bx+c But there are other, and depending on context sometimes mor...
A parabola is given by the equation y2 = -24x.find the directrix and focus of the parabolaFollow • 2 Add comment 1 Expert Answer Best Newest Oldest Arthur D. answered • 05/09/17 Tutor 5.0 (252) Mathematics Tutor With a Master's Degree In Mathematics About this tutor › ...
The focus and directrix of a parabola are (1,2) and 2x-3y+1=0 .Then the equation of the tangent at the vertex is
Since the directrix is vertical, use the equation of a parabola that opens up or down. ( ((x-h))^2=4p(y-k)) Find the vertex. ( (2,-1/2)) Find the distance from the focus to the vertex. ( p=3/2) Substitute in the known values for the variables into the equation(...
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