The equation of the directrix of the parabola x2=8y is View Solution A tangent is drawn to parabola y2=8x which makes angle θ with positive direction of x-axis. The equation of tangent is View Solution The e
Find the equation of circle of radius 3, passing through the origin an... 03:29 Find the length of the latus rectum of the parabola x^(2) = -8y. 00:51 If y^(2) = -12x is the given equation of the parabola, then find the e... 01:35 Find the equation of the parabola with...
The directrix of the parabola is the horizontal line perpendicular to the axis of symmetry. If the axis of symmetry is {eq}x- {/eq} axis, then the directrix of the parabola with the focus {eq}a {/eq}, and the vertex {eq}(h,k) {/eq} is, {eq}x=h \pm a {/eq}. Similarly...
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 ...
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 ...
The geometric definition of a parabola is "the set of points that are equidistant from the focus and the directrix," which is a line that does not pass through the parabola and which is a focal length away from the vertex. Figure 1: Characteristics of a parabola. Vertex, Focus, and Dir...
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-...
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 directrix {eq}y = l {/eq} are given, is found with the help of the standard equation of t...
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.
The directrix and focus of a parabola determine its shape, size, and direction. There is a formula for finding the directrix and focus. Examples...