Write the equation for the parabola given the following information: Vertex (2,2) Directrix at x= -15​

Since the directrix is the vertical line x=4, the axis of the parabola is the horizontal line containing the focus.

So, the axis is the horizontal line y = 0 (the x-axis).

The vertex is on the axis and lies halfway between the focus and directrix.  So, the vertex is (0,0)

Equation of parabola:  (y-0)2 = 4p(x-0).

p is the directed distance between the vertex and focus (since the focus is to the left of the vertex, p < 0.

So, p = -4.   Note:  had the focus been to the right of the vertex, then p would have been positive.  

Equation of parabola:  (y-0)2 = -16(x-0).  Simplify to get y2 = -16x.  

28?

Step-by-step explanation:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)