Finding the equation of parabola

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In summary, the given information of a directrix of x = -1, an axis of y = 2, and a latus rectum of length 2 leads to two possible equations. The vertex can be found at either (-1/2, 1) or (-3/2, 1) depending on the direction of the parabola's opening. The distance from the vertex to the focus is always 1/2 in a parabola.
  • #1
jamescv31
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Greetings, I‘m trying to analyze the given of directrix x = -1, axis y = 2, and latus rectum as 2

I believe there‘s two possibility equations.

I‘m not sure for finding the vertex since I got between ( -.5, 0) and origin itself.
 
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  • #2
I presume that, by "latus rectum as 2", you mean that the length of the latus rectum is 2. In a parabola that is always 4 times the distance from the vertex to the focus so that distance is 1/2. that is also the distance from the vertex to the directrix so the vertex must be at (-1+ 1/2, 1)= (-1/2, 1) (with the parabola opening in the positive x direction) or at (-1- 1/2, 1)= (-3/2, 1) (with the parabola opening in the negative x direction).
 
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  • #3
Yes the length of latus rectum is 2
 

FAQ: Finding the equation of parabola

1. What is a parabola?

A parabola is a U-shaped curve that can be formed by the graph of a quadratic equation. It is a conic section and is one of the most common shapes found in nature.

2. How can I find the equation of a parabola?

To find the equation of a parabola, you need to know the coordinates of at least three points on the curve. Then, you can use the general form of a quadratic equation, y = ax^2 + bx + c, and substitute the coordinates of the points to find the values of a, b, and c.

3. What is the focus and directrix of a parabola?

The focus of a parabola is a fixed point that lies on the axis of symmetry. The directrix is a fixed line that is perpendicular to the axis of symmetry and is located the same distance from the focus as any point on the parabola.

4. Can a parabola have a negative or zero coefficient for the x^2 term?

Yes, a parabola can have a negative or zero coefficient for the x^2 term. This will result in a parabola that opens downwards or is a horizontal line, respectively.

5. Can the vertex of a parabola be located outside of the graph?

No, the vertex of a parabola must always be located on the graph. It is the highest or lowest point on the curve, depending on whether the parabola opens upwards or downwards.

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