Tangents And Normals

Answer (d) 3

Step 1: Differentiate the given function The given curve equation is: Differentiating both sides with respect to : Thus, the slope of the tangent at any point is:
Step 2: Find the slope at Substituting : Since the slope of the normal is the negative reciprocal of the tangent slope, the normal’s slope is:
Step 3: Equation of the normal line The equation of a line with slope passing through a point is given by: Substituting and : Multiplying both sides by 3 to eliminate the fraction: Thus, the correct answer is option (4) .