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-...
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...
When we require the vertex, the equation of the directrix, and the focus, we should modify the given equation, keeping the general equations of the parabola in mind.Answer and Explanation: Consider the provided equation of the parabola, x2+8x−y+6=...
To solve the problem of finding the vertex, focus, directrix, and latus rectum of the parabola given by the equation
The coefficient a in the quadratic equation determines the direction in which the parabola opens. If the coefficient is positive, it opens upward; if negative, the parabola opens downward. 5. Focus and Directrix In the context of conic sections, the focus is a fixed point through which all ...
To find the equation of the parabola given the focus and directrix, we can follow these steps: Step 1: Identify the Focus and DirectrixThe focus of the parabola is given as (0,−3) and the directrix is given as y=3. Step 2: Determine the VertexThe vertex of the parabola lies midwa...
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 )^{...
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Each point on the curve of a parabola is ___ to the focus and the directrix. equidistant equilateral perpendicular tangent Next Worksheet PrintWorksheet 1. A specific parabola is written asy= 2x2- 3x+ 6. This equation is in ___ vertex ...
Step 2: Determine the vertex and parametersFrom the equation (y+3)2=−8(x−1):- The vertex (h,k) is at (1,−3).- The value of 4a is 8, thus a=2. Step 3: Locate the focus and directrixThe focus of the parabola is located at a distance a from the vertex along the ...