what is the parabola of y^2 =28x

The equation y^2 = 28x represents a parabola that opens to the right since the y-variable is squared and is equal to a positive multiple of x. To understand more about this parabola, we can compare it with the standard form of the equation for a parabola that opens to the right, which is:

y^2 = 4ax

Here, 'a' is the distance from the vertex of the parabola to the focus and is also equal to the distance from the vertex to the directrix. To match this with the given equation y^2 = 28x, we can equate:

4a = 28

By solving for 'a', we get:

a = 28 / 4 a = 7

So, the value of 'a' is 7. This tells us that the focus of the parabola is at (7, 0) and the directrix is the line x = -7 when the vertex is at the origin (0, 0). The parabola is symmetric about the y-axis, and its defining characteristic is that every point on the parabola is equidistant from the focus and the directrix.