Question

a parabola has a vertex at (0,0). the focus of the parabola is located on the positive x - axis. which part of the graph will the directrix pass through?
○ the origin
○ the negative part of the x - axis
○ the positive part of the x - axis
○ the negative part of the y - axis

Explanation:

Step1: Recall parabola properties

For a parabola with vertex at \((h,k)\), the focus and directrix are equidistant from the vertex, and lie on the axis of symmetry. Here, vertex is \((0,0)\), focus is on positive \(x\)-axis. So axis of symmetry is \(x\)-axis.

Step2: Determine directrix position

Since focus is on positive \(x\)-axis (distance \(p\) from vertex), directrix is a vertical line (for horizontal parabola) at \(x = -p\), which is on the negative part of \(x\)-axis.

Answer:

B. the negative part of the x - axis