Question

Find the area enclosed between the parabola y² = 4ax and the line y = mx

Answer 1

Given y² = 4ax and line y = mx. 

Points where both meet at a (\(\frac{4a}{m^2}\), \(\frac{4a}{m}\)) and (0,0) 

⇒ y² = 4ax 

m²x² = 4ax ⇒ x = \(\frac{4a}{m^2}\) and y = mx = m.\(\frac{4a}{m^2}\) = \(\frac{4a}{m}\)

Required area = Area of y² = 4ax from 0 to \(\frac{4a}{m^2}\) – Area of the line y = mx from 0 to \(\frac{4a}{m^2}\)