Question

Find the area enclosed between the parabola x² = 4y and the line x = 4y – 2

Answer 1

Given x² = 4y and line x = 4y – 2 

x = x² – 2 

∴ 4y = x² 

x² – x – 2 = 0 

(x – 2) (x + 1) = 0 

⇒ x = 2, y = -1 

So when x = 2, y = 1 ⇒ (2, 1) 

When x = -1, y = \(\frac{1}{4}\) ⇒ (-1, \(\frac{1}{4}\))

These two points where line meets parabola as we got these values by solving the 2 equations, 

So, required area