Question

The area bounded by $y^2=4x$ and the line y = 2x – 4 is

• A. 9
• B. 5
• C. 4
• D. 2

Answer 1

The correct option is A 9



The given curves are $y^2=4x,y=2x-4$
$\Rightarrow (2x-4{)}^2=4x\Rightarrow (x-2{)}^2=x\Rightarrow x^2-4x+4=x$
$\Rightarrow x^2-5x+4=0\Rightarrow (x-1)(x-4)=0\Rightarrow 1,4$
$x=1,4\Rightarrow y=-2,4$
The required region is bounded by
$y^2=4x,y=2x-4$ between the lines $y=-2,y=4$
The required area = ${\int }_{-2}^4[\frac{y+4}{1}-\frac{y^2}{4}]dy={[\frac{y^2}{4}+2y-\frac{y^3}{12}]}_{-2}^4$
$=4+8-\frac{16}{3}-1+4-\frac{2}{3}=15-\frac{18}{3}=9sq.unit$.