Question

If line \( x + y = 0 \) touches the curve \( ax^2 = 2y^2 - b \) at \( (1, -1) \), then the values of \( a \) and \( b \) are respectively

• A. 0, 2
• B. -2, 0
• C. 0, -2
• D. 2, 0

Hint:

For tangent problems, use both the point condition and the slope condition to determine the constants of the equation.

Answer 1

The Correct Option is D

Step 1: Use the condition for tangency.
For the line to be tangent to the curve at \( (1, -1) \), both the point \( (1, -1) \) must satisfy the curve's equation and the slope of the curve at that point must match the slope of the line.
Step 2: Solve for \( a \) and \( b \).
Substituting \( (1, -1) \) into the equation of the curve, we solve for \( a \) and \( b \), and find that \( a = 2 \) and \( b = 0 \).
Step 3: Conclusion.
The correct answer is (D) 2, 0.