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What is the directrix of the parabola y^2 = 8x?
What is the directrix of the parabola y^2 = 8x?
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Practice Questions
1 question
Q1
What is the directrix of the parabola y^2 = 8x?
x = -2
x = 2
y = -4
y = 4
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For the parabola y^2 = 4px, here 4p = 8, so p = 2. The directrix is x = -p = -2.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the directrix of the parabola y^2 = 8x?
Solution:
For the parabola y^2 = 4px, here 4p = 8, so p = 2. The directrix is x = -p = -2.
Steps: 7
Show Steps
Step 1: Identify the equation of the parabola, which is y^2 = 8x.
Step 2: Recognize that the standard form of a parabola that opens to the right is y^2 = 4px.
Step 3: Compare the given equation y^2 = 8x with the standard form y^2 = 4px to find the value of 4p.
Step 4: From the equation y^2 = 8x, we see that 4p = 8.
Step 5: Solve for p by dividing both sides of the equation by 4: p = 8 / 4 = 2.
Step 6: The directrix of a parabola is given by the formula x = -p.
Step 7: Substitute the value of p into the directrix formula: x = -2.
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