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Find the directrix of the parabola y^2 = -8x.
Find the directrix of the parabola y^2 = -8x.
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Practice Questions
1 question
Q1
Find the directrix of the parabola y^2 = -8x.
x = 2
x = -2
x = 4
x = -4
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For the parabola y^2 = 4px, here 4p = -8, so p = -2. The directrix is given by x = -p, which is x = 2.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the directrix of the parabola y^2 = -8x.
Solution:
For the parabola y^2 = 4px, here 4p = -8, so p = -2. The directrix is given by x = -p, which is x = 2.
Steps: 7
Show Steps
Step 1: Identify the standard form of the parabola equation, which is y^2 = 4px.
Step 2: Compare the given equation y^2 = -8x with the standard form to find the value of 4p.
Step 3: In the equation y^2 = -8x, we see that 4p = -8.
Step 4: To find p, divide -8 by 4: p = -8 / 4 = -2.
Step 5: The directrix of a parabola is given by the formula x = -p.
Step 6: Substitute the value of p into the directrix formula: x = -(-2) = 2.
Step 7: Therefore, the directrix of the parabola y^2 = -8x is x = 2.
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