Question

If the line y = 4x – 5 touches the curve y² = ax³ + b at the point (2, 3), find a and b.

Answer 1

y² = ax³ + b

Differentiating both sides w.r.t. x, we get

= slope of the tangent at (2, 3) 

Since, the line y = 4x – 5 touches the curve at the point (2, 3), slope of the tangent at (2, 3) is 4.

2a = 4 ⇒ a = 2

Since (2, 3) lies on the curve y² = ax³ + b

Hence, a = 2 and b = -7.