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What is the general form of the family of curves represented by y^2 = 4ax?
What is the general form of the family of curves represented by y^2 = 4ax?
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Practice Questions
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Q1
What is the general form of the family of curves represented by y^2 = 4ax?
Parabolas opening to the right
Circles with varying centers
Ellipses with varying foci
Hyperbolas with varying asymptotes
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The equation y^2 = 4ax represents a family of parabolas that open to the right with varying values of 'a'.
Questions & Step-by-step Solutions
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Q
Q: What is the general form of the family of curves represented by y^2 = 4ax?
Solution:
The equation y^2 = 4ax represents a family of parabolas that open to the right with varying values of 'a'.
Steps: 5
Show Steps
Step 1: Identify the equation given, which is y^2 = 4ax.
Step 2: Recognize that this equation is a standard form of a parabola.
Step 3: Understand that in this equation, 'a' is a constant that affects the shape and position of the parabola.
Step 4: Note that the parabola opens to the right because the 'y^2' term is positive and 'x' is on the right side of the equation.
Step 5: Realize that different values of 'a' will create different parabolas, all of which open to the right.
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