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runicle
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I am dazed and confused how does 2x^2=y end up being directrix y=-1/8?
Putting the parabola into form [itex]x^2 = 4py[/itex] where p is the focus, will give you the location of the focus, p. Since the points on the parabola are equidistant form the directrix and focus, that should enable you to find the equation of that line.runicle said:I am dazed and confused how does 2x^2=y end up being directrix y=-1/8?
No. [itex]2x^2 = y[/itex] so [itex]x^2 = \frac{1}{2}y[/itex]. In the form [itex]x^2 = 4py[/itex] 4p = 1/2 and p = 1/8. So the focus is (0,1/8). Since the vertex is (0,0) which is equidistant from the focus and the directrix, the directrix is the horizontal line passing through (0,-1/8) ie. y = -1/8runicle said:I don't see the math in it though...
[itex]x^2 = 4py[/itex]
[itex]x/4^2 = py[/itex]
making [itex]x/4^2 = p[/itex]
is it something like that?
A parabola conical whatever equation is a mathematical equation that describes the shape of a parabola that is formed when a cone is cut by a plane parallel to its base. It is often used in physics and engineering to model the trajectory of projectiles or the shape of satellite dishes.
A regular parabola equation has the form y = ax^2 + bx + c, where a, b, and c are constants. On the other hand, a parabola conical whatever equation has the form z = ax^2 + by^2, where z represents the height, x and y represent the coordinates on the base, and a and b are constants that determine the shape of the parabola.
Parabola conical whatever equations are used in various fields such as physics, engineering, and architecture. They are used to model the shape of satellite dishes, the trajectory of projectiles, and the design of bridges and arches, among others.
To graph a parabola conical whatever equation, you can plot points by substituting different values for x and y and then connecting them with a smooth curve. Alternatively, you can use a graphing calculator or software to graph the equation.
Yes, there are many real-life examples of parabola conical whatever equations. Some examples include the shape of a satellite dish, the trajectory of a thrown ball, the design of arches and bridges, and the shape of a water fountain. These equations are also used in physics and engineering to model various phenomena.