The equation of the tangent at (2, 3) on the curve y2 = ax3 + b is y

1.	The equation of the tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and b.
Answer» Given as y² = ax³ + b is y = 4x – 5 Differentiate the given curve, to get the slope of tangent 2y(dy/dx) = 3ax² dy/dx = 3ax²/2y m(tangent) at (2, 3) = 2a The equation of tangent is given by y – y₁ = m (tangent) (x – x₁) Comparing the slope of a tangent with the given equation 2a = 4 a = 2 (2, 3) lies on the curve, these points must satisfy 3² = 2 × 2³ + b b = – 7

The equation of the tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and b.

Answer»

Given as y² = ax³ + b is y = 4x – 5

Differentiate the given curve, to get the slope of tangent

2y(dy/dx) = 3ax²

dy/dx = 3ax²/2y

m(tangent) at (2, 3) = 2a

The equation of tangent is given by y – y₁ = m (tangent) (x – x₁)

Comparing the slope of a tangent with the given equation

2a = 4

a = 2

(2, 3) lies on the curve, these points must satisfy

3² = 2 × 2³ + b

b = – 7