Question

If the line $ x - 1 = 0 $ is the direction of the parabola $ y^2 - kn + 8 = 0 $, then one of the values of $ k $ is

• A. \( \frac{1}{8} \)
• B. \( 8 \)
• C. \( 4 \)
• D. \( \frac{1}{4} \)

Hint:

When dealing with parabolas, equate the given equation to the standard form \( y^2 = 4ax \) to find the value of constants.

Answer 1

The Correct Option is A

We are given the equation of the parabola: \[ y^2 - kn + 8 = 0 \]
Step 1: Standard form of a parabola
The standard equation of a parabola is \( y^2 = 4ax \), where \( a \) is the distance from the vertex to the focus.
Step 2: Equate the given equation to standard form
Comparing the given equation \( y^2 - kn + 8 = 0 \) with \( y^2 = 4ax \), we see that \( kn = 4a \). Thus, we find \( k = \frac{1}{8} \).
Step 3: Conclusion
The value of \( k \) is \( \frac{1}{8} \), corresponding to option (a).