Question

The equation of one of the common tangents to the parabola \( y^2 = 8x \) and \( x^2 = 4y - 4 \) is

• A. \( y = x^2 \)
• B. \( y = x - 2 \)
• C. \( y = x + 2 \)
• D. None of these

Hint:

The equation of a common tangent can be found by using the tangent conditions for both curves and solving the system.

Answer 1

The Correct Option is B

Step 1: Find the equation of the tangent.
To find the common tangent to the given parabolas, we apply the tangent condition for both parabolas. After solving, we get the equation of the tangent as \( y = x - 2 \).
Step 2: Conclusion.
The correct answer is (B), \( y = x - 2 \).