Question

If \((2,0)\) is the vertex and \(y\)-axis is the directrix of a parabola, then its focus is

• A. \((2,0)\)
• B. \((-2,0)\)
• C. \((4,0)\)
• D. \((-4,0)\)

Hint:

The vertex of a parabola is exactly midway between the focus and the directrix.

Answer 1

The Correct Option is C

Step 1: The directrix is the \(y\)-axis: \[ x=0 \]

Step 2: Vertex is: \[ (2,0) \]

Step 3: The vertex lies midway between focus and directrix.

Step 4: Since the directrix is \(x=0\) and vertex has \(x=2\), the focus must be at the same distance on the other side: \[ x=4 \]

Step 5: Hence focus is: \[ (4,0) \] \[ \boxed{(4,0)} \]