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 ...
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...
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 ...
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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