# 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. (CBSE 2016)

finding the slope of the tangent by differentiating the curve

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

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