Question

Which equation represents a parabola opening to the right with a vertex at the origin and a focus at (4, 0)?

a: x=1/8 y²
b: 1/16 y²
c: -1/8 y²
d:-1/15 y²

Answer 1

The correct equation for a parabola opening to the right with its vertex at the origin and focus at (4, 0) is x = 1/16 y².

Step-by-step explanation:

The equation that represents a parabola opening to the right with a vertex at the origin and a focus at (4, 0) is x = ⅛ y² (option a). A parabola that opens to the right has the form x = ay², where a is a positive constant that determines the width of the parabola. The focus of a parabola (h, k + 1/4a) for a rightward-opening parabola, is ⅛ units from the vertex along the axis of symmetry. By substituting the focus coordinates into the vertex-form equation of a parabola, we can find that a = 1/16. Therefore, the correct parabola equation opening to the right with the given vertex and focus is x = 1/16 y² (option b).