assume point (a, b) which lies on the given curve

finding the slope of the tangent by differentiating the curve

m(tangent) at (a,b) is

Since this tangent passes through , its slope can also be written as

Equating both the slopes as they are of the same tangent

b² = 3a² – 4a …(i)

Since points (a,b) lies on this curve

3a² – b² = 8 …(ii)

Solving (i) and (ii) we get

3a² – 8 = 3a² – 4a

a = 2

b = 2 or – 2

therefore points are (2,2) or (2, – 2)

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

y – 2 = 3(x – 2)

or

y + 2 = – 3(x – 3)