Question

The focal distance of the point \( (4, 4) \) on the parabola with vertex at \( (0, 0) \) and symmetric about the y-axis is

• A. 4
• B. 5
• C. \( 5\sqrt{2} \)
• D. \( 4\sqrt{2} \)

Hint:

For a parabola symmetric about the y-axis with vertex at \( (0, 0) \), use the equation \( y^2 = 4ax \) to find the focal distance.

Answer 1

The Correct Option is B

Step 1: Equation of the parabola.
The equation of a parabola symmetric about the y-axis with vertex at \( (0, 0) \) is of the form \( y^2 = 4ax \). Given that the point \( (4, 4) \) lies on the parabola, we substitute into the equation: \[ 4^2 = 4a(4) \quad \Rightarrow \quad 16 = 16a \quad \Rightarrow \quad a = 1 \]
Step 2: Focal distance.
The focal distance is given by \( f = a \), and since \( a = 1 \), the focal distance is 5.
Step 3: Conclusion.
Thus, the focal distance is 5, corresponding to option (B).