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...
How does one write a quadratic equation using the directrix and focus? 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 ...
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...
A parabola refers to an equation of a curve, such that each point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the "focus" of the parabola, and the fixed line is called the "directrix" of the parabola. Also, an important point to ...
Find the standard form of the equation of the parabola using the information given. Focus: {eq}(0, 13) {/eq} Directrix: {eq}y = -13 {/eq} The Equation of the Parabola: The equation of the parabola when its focus {eq}(p,q) {/eq} and...
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 ...
Finally, notice that the distance from the focus to the vertex is equal to the distance from the vertex to the directrix.Using the definition of a parabola to find the equation of a parabola.Write an equation for a graph that is the set of all points in the plane that are at the same...
Real-world situations can be modeled using the standard equations of parabolas. 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...
A parabola given inisy=a(x−h)2+k. This has vertex(h,k)and focus(h,k+14a). A parabola can also be givenas4p(y−k)=(x−h)2. This has vertex(h,k)and directrixy=k−p. It is important to know how toto turn a quadratic equation into vertex ...
a conic section formed by the intersection of a cone by a plane parallel to its side. Standard equation:y2= 4ax, where 2ais the distance between focus and directrix Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005 ...