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» finding the slope of the tangent by differentiating the curve \(2y\frac{dy}{dx}=3ax^2\) \(\frac{dy}{dx}=\frac{3ax^2}{2y}\) m(tangent) at (2,3) = 2a equation of tangent is given by y – y₁ = m(tangent)(x – x₁) now comparing the slope of a tangent with the given equation 2a = 4 a = 2 now (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»

finding the slope of the tangent by differentiating the curve

\(2y\frac{dy}{dx}=3ax^2\)

\(\frac{dy}{dx}=\frac{3ax^2}{2y}\)

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

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

now comparing the slope of a tangent with the given equation

2a = 4

a = 2

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

3² = 2 × 2³ + b

b = – 7