Question

The line \( 2x + \sqrt{6}y = 2 \) is tangent to the curve \( x^2 - 2y^2 = 4 \). The point of contact is

• A. \( (4, -6) \)
• B. \( (3, -6) \)
• C. \( (7, -6) \)
• D. \( (2, -6) \)

Hint:

To find the point of contact between a line and a curve, solve the system of equations formed by the line equation and the curve equation.

Answer 1

The Correct Option is A

Step 1: Finding the point of contact.
The equation of the line and the curve are used to find the point of contact by substituting the values and solving the system of equations.

Step 2: Conclusion.
The point of contact is \( (4, -6) \), corresponding to option (1).