Find the equation of the parabola with focus(−3,0)and the equation of the directrix is x = 3. Find the equation of the parabola with focus (7, 0) and equation of the directrix is x = -7. View Solution FInd the equation of the parabola The focus at (1,1) the directrixx−y...
Find the vertex, focus, and the equation of the directrix for the parabola: x = 4y^2 - 8y + 2 Find the vertex, the focus and equation of the directrix for the parabola whose equation is y^{2} + 12x = 0. Find the vertex, focus, and directri...
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-...
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 the parabola as given below: {eq}\left ( y-k \right )^{2}...
A parabola is the set of all points M(x,y) in a plane such that the distance from M to a fixed point F called the focus is equal to the distance from M to a fixed line called the directrix as shown below in the graph. Let us consider a parabola with a vertex V(0,0) (the...
Find the equation of hyperbola whose equation of directrix is x+2y=1, focus is (-1,-1) and eccentricity is√2. View Solution Find the equation of the parabola whose focus is (2, 0) and directrix isx=−2. View Solution Find the equation of the hyperbola whose : focus is (2,2)...
Learn to find the equation of a parabola given its focus and directrix. Understand the standard equation of a parabola and learn to solve related...
parabola The parabola at left is formed by graphing the function y = x2. pa·rab·o·la (pə-răb′ə-lə) The curve formed by the set of points in a plane that are all equally distant from both a given line (called the directrix) and a given point (called the focus) tha...
From the focal point to the fixed, straight line of the directrix, these are the parabola components that define the shape and properties of the curve. 1. Vertex The vertex is the parabola's minimum or maximum value. It serves as the focal point for both the axis of symmetry and the pa...
Learn to find the equation of a parabola with examples. Understand the equation of a parabola in standard form and the properties and applications...