Question

A straight line parallel to the line \( 2x + y - 5 = 0 \) is also a tangent to the curve \( y^2 = 4x + 5 \). Then the point of contact is

• A. (2, 1)
• B. (-1, 1)
• C. (-1, -1)
• D. (3, 4)

Hint:

When finding the point of tangency, use the condition that the slope of the tangent is equal to the derivative of the curve at the point.

Answer 1

The Correct Option is C

Step 1: Write the equation of the tangent.
For the given curve \( y^2 = 4x + 5 \), the equation of the tangent is derived from the general form and slope condition for tangency.
Step 2: Conclusion.
Thus, the point of contact of the tangent to the curve is (-1, -1).
Final Answer: \[ \boxed{(-1, -1)} \]