To solve the problem, we need to find the equation of the parabola given its vertex and directrix, and then determine the values ofa,b,c,d, andkin the standard form of the parabola equation. Finally, we will co
The equation of the parabola is (x−h)2+(y−k)2=(ax+by+c)2a2+b2, where (h,k) is the focus of the parabola and ax+by+c=0 is the directrix. If two lines are perpendicular each other, the slopes of the lines will be m1m2=−1 ...
Directrix: . Axis of symmetry: Figure 2. Properties of parabolas.Example 2 Graph . State which direction the parabola opens and determine its vertex, focus, directrix, and axis of symmetry. The equation is the same as . Since a < 0 and the parabola opens horizontally, this parabola open...
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 -...
The given equation of the parabola is of the form: (x−h)2=4a(y−k) The coordinates of the vertex will be: (h,k) The coordinates of focus is (h,k+a) The equation of the directrix: y=k−a Answer and Explanation:1
Answer: Length of latus rectum = 1/2, focus = (193/8, 3), Vertex = (24,3) Example 3. Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = 4? Solution: Given that, Focus = (0, 0) and directrix y = 4 Let us suppose that there is a ...
For instance, given the diameter and focus of a cross-section of a parabolic reflector, we can find an equation that models its sides.Glossarydirectrix a line perpendicular to the axis of symmetry of a parabola; a line such that the ratio of the distance between the points on the conic ...
geometry parabola define a parabola Calling Sequence Parameters Description Examples Calling Sequence parabola( p , [ A , B , C , E , F ], n ) parabola( p , ['focus'=fou, 'vertex'=ver], n ) parabola( p , ['directrix'=dir, 'focus'=fou], n ) parabola(...
The equation x2 = 16y is in standard form. We can again use the definition of a parabola to find the standard form of the equation of a parabola with its vertex at the origin. Place the focus at the point (0, p). Then, the directrix has an equation given by y = -p....
For a parabola whose axis is thex-axis and with vertex at the origin, the equation isy2= 2px, in whichpis the distance between the directrix and the focus. In more general cases, the equation of a parabola can be written asy=ax2+bx+c, wherea,b, andcare constants that determine the...