# Thread: areas bounded by curves

1. ## areas bounded by curves

I have to find the area of the area bound by y^2=4x and y=2x-4

I have to find the points of intersection. would I do this by solving 2x-4 = 4x or by 2x-4 = sqrt(4x) or both?

2. No, y is not equal to y^2! You can write y= sqrt(4x)= 2sqrt(x) and set that equal to 2x- 4. But it might be simpler to write x= y^2/4 so that y= 2(y^2/4)- 4= y^2/2- 4 and solve that quadratic equation.

3. im slightly confused by the response. what would a, b ,and c be then for the quadratic equation. well c = -4, but what would a and b be?

4. I keep getting x=4, but there should be another one that is x=-2 according to the back of the book. because the interval is -2<x<4

No. This is the integral $\int_{ - 2}^4 {\left( {\frac{{y + 4}}{2} - \frac{{y^2 }}{4}} \right)dy}$.
Because the two curves meet at $(1,-2)~\&~(4,4)$.
Just solve $(2x-4)^2=4x$.