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Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1?
The first thing to do is to decide which way up this is and whether its a side ways one or not. Clearly there are 4 different types open up or down or open to the left or right.
The focus is inside the parabola and the directrix is a line on the outside but the same distance from the vertex as the vertex is from the focus.
Because the focus is above the directrix then this is a parabola that opens upwards and has an equation that has an x²
4p(y – k) = (x – h)² is the general form of an opening up or down one
p is the distance from the directrix to the vertex or twice the distance from the directrix to the focus
(h,k) is the co-ords of the vertex
2|p| = 2 so |p| = 1 (the focus is at y = 1 and the directrix is y = -1) difference 2 (1- – 1)
but because we are facing upwards p = 1 (ie its positive. It would be -ve if it pointed downwards)
Vertex is at (0,0) the y co-ord is halfway between the focus and the directrix
The x bit is 0 for the focus and the vertex so the equation becomes
so 4(y – 0) = (x – 0)²
4(y) = (x)²
y = 1/4x²
This is about as simple as it could be as the vertex is at the origin (0,0)
You would get x terms if the vertex was not at the origin
Find the Parabola with Focus (0,4) and Directrix y=4 (0,4 – Find the Parabola with Focus (0,4) and Directrix y=4 (0,4) y=4. Since the directrix is vertical, use the equation of a parabola that opens up or down. Find the vertex. Tap for more steps… The vertex is halfway between the directrix and focus. Find the coordinate of the vertex using the formula.the focus, (0;p) and directrix, y= p, we derive the equation of the parabolas by using the following geometric de nition of a parabola: A parabola is the locus of points equidistant from a point (focus) and line (directrix).Correct answers: 1 question: Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1. (2 points)
PDF Final Project – Deriving Equations for Parabolas – Find the Parabola with Focus f(0,-5) and Directrix y=5 (0,-5) ; y=5 Since the directrix is vertical , use the equation of a parabola that opens up or down. Find the vertex .Question: Or Equation Do You Need When Deriving The Equation Of The Parabola With Focus (-4,1) And Directrix Y=5? (1 Point) X – A) = 4y – ) (y- K = 4(x – H) 15. What Is The P-value Of The Parabola With Focus (-6, 5) And Directrix X=0? (1 Point) 1 3 6 12 16.x 2 + y 2 − 2xy + 8x + 8y − 16 = 0 Let P ( x , y ) be any point on the parabola whose focus is S (0, 0) and the directrix is x + y = 4. Draw PM perpendicular to x + y = 4.
Derive the equation of the parabola with a focus at (0, 1 – If the focus is at (0,-4) and the directrix is y = 4 then the vertex of the parabola is midway between these two features at (0,0). The parabola is thus a downward opening parabola with the standard equation x² = 4cy where c is the distance from the vertex to the focus. In this question, c = -4.👍 Correct answer to the question Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1 – e-eduanswers.comLearn how to write the equation of a parabola given the focus and the directrix. A parabola is the shape of the graph of a quadratic equation. A parabola can…