What is the equation of the parabola with vertex at the origin and the focus at 0 4?

A General Note: Standard Forms of Parabolas with Vertex (0, 0)

Axis of Symmetry	Equation	Focus
x-axis	y2=4px	(p, 0)
y-axis	x2=4py	(0, p)

What is an equation of the parabola with vertex at the origin and focus − 5 0?

Explanation: Focus is at (5,0) and vertex is at (0,0) . the equation of parabola is y2=4ax , a=5 is the focal distance (the distance from vertex to focus).

How do you find the axis of a parabola?

Find the vertex, focus, the equation of directrix and length of the latus rectum of the parabola y 2 = -12x. Given equation of parabola is y 2 = -12x … (i) This equation has y 2 term. So the axis of the parabola is the x-axis. Focus is (-a,0) = (-3,0).

What is a similar derivation of the equation of a parabola?

A similar derivation gives us: Equation of a parabola in terms of the focus. p is the distance from the vertex to the focus and vertex to the directrix. Focus form of the equation of a parabola. p is the distance from the vertex to the focus and vertex to the directrix.

How to write the equation of parabola in standard form?

Now, let us write the equation of parabola in standard form when the vertex is not at the origin and the axis of symmetry is parallel to the x-axis or y-axis. These are tabulated as given below: Example 1: Find the coordinates of the focus, axis, the equation of the directrix and latus rectum of the parabola y 2 = 12x.

What is the equation of the parabola in focus vertex form?

The equation of the parabola in focus vertex form is (x – h) 2 = 4p (y – k) The vertex is at (h,k) giving us h = 4, k = 6 The focus is located at (h, k + p). In this example the focus is at (4, 3) so k + p = 3.