If the tangent to the curve y² = ax³ at (a, a) makes an angle of 45° with the x-axis, then a equals: A. 3/2 B. 1/2 C. 2/3 D. 3 Answer: A) 3/2 Explanation: y² = ax³ → 2y dy/dx = 3ax² → dy/dx = 3ax²/(2y). At (a, a), slope = 3a(a²)/(2a) = 3a/2. tan 45° = 1 → 3a/2 = 1 → a = 2/3.

imo class 12 application of derivatives

If the tangent to the curve y² = ax³ at (a, a) makes an angle of 45° with the x-axis, then a equals:

VAVidaara Admin Asked 6d ago 0 views 0 answers

If the tangent to the curve y² = ax³ at (a, a) makes an angle of 45° with the x-axis, then a equals:

Answer: A) 3/2

Explanation: y² = ax³ → 2y dy/dx = 3ax² → dy/dx = 3ax²/(2y). At (a, a), slope = 3a(a²)/(2a) = 3a/2. tan 45° = 1 → 3a/2 = 1 → a = 2/3.