Q. 85.0( 1 Vote )

# The equation of the tangent at (2, 3) on the curve y^{2} = ax^{3} + b is y = 4x – 5. Find the values of a and b.

Answer :

finding the slope of the tangent by differentiating the curve

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

equation of tangent is given by y – y_{1} = m(tangent)(x – x_{1})

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

3^{2} = 2 × 2^{3} + b

b = – 7

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