Before we begin, note that in the given equation the variable that is raised to the second power is y.
y^2=2/5x
Therefore, the axis of symmetry of the parabola is a horizontal line.
Finding the Desired Information
Let's recall the general form of the equation for this type of parabola.
x=1/4 p(y- k)^2+ h
Let's rearrange the given equation.
We need to identify the values of h, k, and p. Let's start with p. To do so, we will solve the equation 14 p= 52. We set it equal to 52 because it is the coefficient of the y^2 term.
Knowing that p= 110, we can rewrite the equation.
x=5/2y^2
⇕
x=1/4( 1/10)(y- 0)^2+ 0
Now we have that h= 0, k= 0, and p= 110. By recalling the corresponding formulas, we can find the focus, directrix, and axis of symmetry of the parabola.
Focus
Directrix
Axis of Symmetry
Formula
( h+ p, k)
x= h- p
y= k
Value
( 0+ 1/10, 0) ⇓ (1/10,0)
x= 0- 1/10 ⇓ x=- 1/10
y= 0
Drawing the Parabola
Now, let's draw the parabola using the obtained information.
