Question

If the line \( 2x - 3y = k \) touches the parabola \( y^2 = 6x \), then find the value of \( k \).

• A. \( -15/4 \)
• B. \( -7/4 \)
• C. \( -2/4 \)
• D. \( -1/4 \)

Hint:

For a line to be tangent to a curve, the discriminant of the quadratic formed by substitution must be zero.

Answer 1

The Correct Option is A

Step 1: Use the condition for tangency.
For a line to be tangent to the parabola, the discriminant of the quadratic equation formed by substituting the line equation into the parabola equation must be zero.
Step 2: Conclusion.
By solving the discriminant condition, we find that \( k = -15/4 \). Final Answer: \[ \boxed{-\frac{15}{4}} \]