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The family of curves given by y^2 = 4ax represents which type of conic section?
The family of curves given by y^2 = 4ax represents which type of conic section?
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The family of curves given by y^2 = 4ax represents which type of conic section?
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The equation y^2 = 4ax represents a parabola that opens to the right.
Questions & Step-by-step Solutions
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Q: The family of curves given by y^2 = 4ax represents which type of conic section?
Solution:
The equation y^2 = 4ax represents a parabola that opens to the right.
Steps: 5
Show Steps
Step 1: Identify the equation given, which is y^2 = 4ax.
Step 2: Recognize that this equation is in the standard form of a parabola.
Step 3: Note that in the equation y^2 = 4px, the variable y is squared and the variable x is not, indicating a vertical orientation.
Step 4: Since the equation is y^2 = 4ax, it shows that the parabola opens to the right because 'a' is positive.
Step 5: Conclude that the family of curves represented by this equation is a parabola that opens to the right.
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