Application of Integrals

Let S denote the locus of the mid-points of those chords of the parabola y2=x, such that the area of the region enclosed between the parabola and the chord is 43. Let R denote the region lying in the first quadrant, enclosed by the parabola y2=x, the curve S, and the lines x=1 and x=4. Then which of the following statements is (are) TRUE?

1. (4, 3) S
2. (5, 2) S
3. Area of R is 143-2 3
4. Area of R is 143- 3

Let S= \(x,y) R R: x 0, y 0, y2 4x, y2 12-2x and 3y+ 8 x 5 8 \. If the area of the region S is 2, then is equal to

1. 172
2. 173
3. 174
4. 175