Final answer:
The equations x=5y^2 and x=3y^2 describe parabolas oriented along the x-axis. The parabola for x=5y^2 is narrower than the one for x=3y^2 because it has a larger coefficient, causing a steeper opening from the origin.
Step-by-step explanation:
The equations given, x=5y^2 and x=3y^2, both represent parabolas that are oriented along the x-axis since the independent variable y is squared.
The coefficient in front of y^2 affects the 'width' of the parabola. A larger coefficient means the parabola is narrower because the value of x increases more rapidly as y increases.
In comparing the two parabolas described by the given equations, the parabola represented by x=5y^2 will be narrower than the parabola represented by x=3y^2 because 5 is greater than 3, causing x to increase more quickly for the same value of y in the former equation.
Both parabolas share the same vertex at the origin (0,0), and they both open to the right since x is directly proportional to y squared. However, because the coefficient (multiplier of y^2) is different for each equation, the rate at which they open out from the vertex varies, with the parabola for x=5y^2 opening more steeply compared to the one for x=3y^2.