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How do you write an equation of a parabola with vertex at the origin and the given focus 60?
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What is the standard equation for vertex at origin opens down 1 and 76 units between the vertex and focus?
Since the vertex is at the origin and the parabola opens downward, the equation of the parabola is x2 = 4py, where p < 0, and the axis of symmetry is the y-axis. So the focus is at y-axis at (0, p) and the directrix equation is y = -p. Now, what do you mean with 1 and 76 units? 1.76 units? If the distance of the vertex and the focus is 1.76 units, then p = -1.76, thus 4p = -7.04, then the equation of the parabola is x2 = -7.04y.
What does 4 stands for in equation of parabola square of square of y equals 4ax?
A parabola with an equation, y2 = 4ax has its vertex at the origin and opens to the right. It's not just the '4' that is important, it's '4a' that matters. This type of parabola has a directrix at x = -a, and a focus at (a, 0). By writing the equation as it is, the position of the directrix and focus are readily identifiable. For example, y2 = 2.4x doesn't say a great deal. Re-writing the equation of the parabola as y2 = 4*(0.6)x tells us immediately that the directrix is at x = -0.6 and the focus is at (0.6, 0)
How do you solve parabola equation having lb focus at 0 3?
There is not enough information. You need either the directrix or vertex (or some other item of information).
The co-ordinates of the focus of Parabola x minus 3 power 2 is equal to 4 y minus 2 is Answer is 3 3 how?
The standard equation for an upward opening parabola with its vertex at (f,g) is (x - f)2 = 4c(y - g), where c is the focal length, that is the distance of the focus from the vertex. Putting the equation shown in this form we have :- (x - 3)2 = 4 * 1(y - 2) . . . thus c = 1 The vertex is at (3,2) and as the focal length is 1 (and this is positive) then the coordinates of the focus are (3, [2 + 1]) = (3,3).
What happens to the shape of a parabola as the distance between the vertex of the curve and the focus becomes very large?
The parabola shape is magnified. If you keep the same scale for the graph, the parabola will look wider, more flattened out.
What is the equation of a parabola with a vertex at 0 0 and a focus at 0 6?
The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y
What is the standard equation of a parabola that opens up or down and whose vertex is at the origin?
focus , directrix
What is the standard equation for vertex at origin opens down 1 and 76 units between the vertex and focus?
Since the vertex is at the origin and the parabola opens downward, the equation of the parabola is x2 = 4py, where p < 0, and the axis of symmetry is the y-axis. So the focus is at y-axis at (0, p) and the directrix equation is y = -p. Now, what do you mean with 1 and 76 units? 1.76 units? If the distance of the vertex and the focus is 1.76 units, then p = -1.76, thus 4p = -7.04, then the equation of the parabola is x2 = -7.04y.
What is the equation of a prabola with the vertex 0 0 and focus 0 4?
x2 = 16y The standard formula for a parabola with its vertex at the origin (0, 0) and a given focus (and the y-axis as an axis of symmetry) is as follows: x2 = 4cy In this case, the c is the y value of the focus. The focus in this case was (0, 4), and the y value in the focus is 4. That makes the c = 4. Further, that makes the equation for this parabola x2 = 4 (c)y = 4 (4)y = 16y Given that the vertex was the origin, (0, 0), and the focus is (0, 4), we can conclude that the axis of symmetry is the y-axis because the y value of the focus is 0. We can also conclude that the parabola opens up, because the focus has a positive y value.
What does 4 stands for in equation of parabola square of square of y equals 4ax?
A parabola with an equation, y2 = 4ax has its vertex at the origin and opens to the right. It's not just the '4' that is important, it's '4a' that matters. This type of parabola has a directrix at x = -a, and a focus at (a, 0). By writing the equation as it is, the position of the directrix and focus are readily identifiable. For example, y2 = 2.4x doesn't say a great deal. Re-writing the equation of the parabola as y2 = 4*(0.6)x tells us immediately that the directrix is at x = -0.6 and the focus is at (0.6, 0)
What is the extreme point of a parabola that is located halfway between the focus and directrix called?
It is the vertex of the parabola.
The vertex is the extreme point of a parabola and is located halfway between the focus and?
focus directrix
The is the extreme point of a parabola and is located halfway between the focus and directrix?
The vertex -- the closest point on the parabola to the directrix.
What is the equation of a parabola with vertex at 1 -3 and focus at 2 -3?
For a parabola with an axis of symmetry parallel to the x-axis, the equation of a parabola is given by: (y - k)² = 4p(x - h) Where the vertex is at (h, k), and the distance between the focus and the vertex is p (which can be calculated as p = x_focus - x_vertex). For the parabola with vertex (1, -3) and focus (2, -3) this gives: h = 1 k = -3 p = 2 - 1 = 1 → parabola is: (y - -3)² = 4×1(x - 1) → (y + 3)² = 4(x - 1) This can be expanded to: 4x = y² + 6y + 13 or x = (1/4)y² + (3/2)y + (13/4)
What is the focus of a parabola?
The focus of a parabola is a fixed point that lies on the axis of the parabola "p" units from the vertex. It can be found by the parabola equations in standard form: (x-h)^2=4p(y-k) or (y-k)^2=4p(x-h) depending on the shape of the parabola. The vertex is defined by (h,k). Solve for p and count that many units from the vertex in the direction away from the directrix. (your focus should be inside the curve of your parabola)
How do you solve parabola equation having lb focus at 0 3?
There is not enough information. You need either the directrix or vertex (or some other item of information).
The vertex is the extreme point of a parabola and is located halfway between the and directrix?
focus
