To determine the direction in which the parabola defined by the equation [tex]\( x = 5y^2 \)[/tex] opens, let's analyze the given equation step by step.
1. Understanding the General Form:
The equation [tex]\( x = 5y^2 \)[/tex] is a variation of the general form of a parabolic equation that opens horizontally. The general equation for such a parabola is [tex]\( x = ay^2 \)[/tex].
2. Coefficient Analysis:
- In the given equation [tex]\( x = 5y^2 \)[/tex], the coefficient [tex]\( a \)[/tex] is 5.
- The sign and value of [tex]\( a \)[/tex] play a crucial role in determining the opening direction of the parabola.
3. Behavior Based on the Coefficient:
- When [tex]\( a > 0 \)[/tex] (i.e., [tex]\( a \)[/tex] is positive), the parabola opens to the right.
- When [tex]\( a < 0 \)[/tex] (i.e., [tex]\( a \)[/tex] is negative), the parabola opens to the left.
4. Application to the Given Equation:
- In our equation [tex]\( x = 5y^2 \)[/tex], the coefficient [tex]\( a \)[/tex] is 5, which is greater than 0.
- Since 5 is positive, the parabola will open to the right.
Therefore, the direction in which the parabola defined by the equation [tex]\( x = 5y^2 \)[/tex] opens is:
C. right
