What is the equation of the directrix of the parabola x^2 = 8y?
Practice Questions
1 question
Q1
What is the equation of the directrix of the parabola x^2 = 8y?
y = -2
y = 2
x = -4
x = 4
The directrix of the parabola x^2 = 8y is y = -2.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the equation of the directrix of the parabola x^2 = 8y?
Solution: The directrix of the parabola x^2 = 8y is y = -2.
Steps: 6
Step 1: Identify the standard form of the parabola. The equation x^2 = 8y is in the form x^2 = 4py, where p is the distance from the vertex to the focus and also to the directrix.
Step 2: Compare the given equation x^2 = 8y with the standard form x^2 = 4py. Here, 4p = 8.
Step 3: Solve for p by dividing both sides of the equation 4p = 8 by 4. This gives p = 2.
Step 4: Determine the vertex of the parabola. The vertex of the parabola x^2 = 8y is at the origin (0, 0).
Step 5: Find the equation of the directrix. The directrix is located p units below the vertex for a parabola that opens upwards. Since p = 2, the directrix is at y = 0 - 2.
Step 6: Write the equation of the directrix. Therefore, the equation of the directrix is y = -2.
