Focus: (2,0) Directrix: x=- 2 Axis of Symmetry: y=0 Graph:
Practice makes perfect
Before we begin, note that in the given equation the variable that is raised to the second power is y.
x=1/8y^2
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
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= 18. We set it equal to 18 because this is the coefficient of the y^2-term.
Knowing that p= 2, we can rewrite the equation.
x=1/8y^2
⇕
x=1/4( 2)(y- 0)^2+ 0
Now we have that h= 0, k= 0, and p= 2. 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+ 2, 0) ⇓ (2,0)
x= 0- 2 ⇓ x=- 2
y= 0
Drawing the Parabola
Now, let's draw the parabola using the obtained information.
