Question

A parabola has the origin as its focus and the line \( x = 2 \)  as the directrix. Then the vertex of the parabola is at:

• A. \( (0, 2) \)
• B. \( (1, 0) \)
• C. \( (0, 1) \)
• D. \( (2, 0) \)

Hint:

The vertex of a parabola is always halfway between the focus and the directrix.

Answer 1

The Correct Option is B

The vertex of a parabola lies halfway between the focus and the directrix. 
The focus is at the origin \( (0, 0) \) and the directrix is the line \( x = 2 \). 
The midpoint between these points is at \( \left( \frac{0 + 2}{2}, \frac{0 + 0}{2} \right) = (1, 0) \). Thus, the vertex of the parabola is at \( (1, 0) \).