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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

WRITE THE EQUATION OF THE PARABOLA with a directrix of y=1 – -4y = x², or y = – x²/4, or y = -(1/4)x². Step-by-step explanation: Because the focus is beneath the directrix, this vertical parabola opens down. The general formula is 4py = x². Because the distance between focus and directrix is 2 units, p = -1 here. The negative sign shows that the parabola opens down.Find the equation to the parabola with focus (3, − 4) and directrix 6 x − 7 y + 5 = 0. View solution Equation of parabola having the extremities of its latus rectum as ( − 4 , 1 ) and ( 2 , 1 ) isDerive the equation of the parabola with a focus at (0, 1) and a directrix of y = 1. View the step-by-step solution to: Question

Find the equation of parabola whose Focus is (1, 1) and – 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 originThe equation of parabola with vertex $(0,0)$, passing through $(-2,8)$ and axis that coincides with the y-axis is:Find the Parabola with Focus (2,-1) and Directrix y=-1/2 (2,-1) y=-1/2. 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.

[Solved] Derive the equation of the parabola with a focus – 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).Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1. (2 points) A. f(x) = − … Get the answers you need, now! anamfarrant anamfarrant 07/10/2018 Mathematics College answered • expert verified Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1.Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1? f(x) = −one half (x − 6)^2 + three halves. 1 0. Still have questions? Get your answers by asking now. Ask Question + 100. Join Yahoo Answers and get 100 points today. Join. Trending Questions.