Question

If the parabola \( y^2 = 4ax \) passes through the point \( (1, -2) \), then the tangent at this point is:

• A. \( x + y - 1 = 0 \)
• B. \( x + y + 1 = 0 \)
• C. \( x + y + 11 = 0 \)
• D. \( x + y - 11 = 0 \)

Hint:

The equation of a tangent to a parabola can be derived by using the general formula for the tangent at any point on the curve.

Answer 1

The Correct Option is B

Step 1: The equation of the parabola is \( y^2 = 4ax \), and the point \( (1, -2) \) lies on the parabola.
Step 2: The equation of the tangent to the parabola at any point \( (x_1, y_1) \) is given by: \[ yy_1 = 2a(x + x_1). \] Substituting \( x_1 = 1 \) and \( y_1 = -2 \), the tangent equation becomes \( x + y + 1 = 0 \).

Final Answer: \[ \boxed{x + y + 1 = 0} \]