**??? - 2016 Q7**

8

Fig. 8 shows the curve

The curve has an asymptote

The tangent to the curve at the origin O crosses the line

Fig. 8 shows the curve

*y*=*x/√ (x+4)*and the line*x*= 5.The curve has an asymptote

*l*.The tangent to the curve at the origin O crosses the line

*l*at*P*and the line*x*= 5 at*Q*.(i) Show that for this curve d

(ii) Find the coordinates of the point P. [4]

(iii) Using integration by substitution, find the exact area of the region enclosed by the curve, the tangent OQ and the line

*y*/d*x*=*x*+8/2(x+4)^{3/2}[5](ii) Find the coordinates of the point P. [4]

(iii) Using integration by substitution, find the exact area of the region enclosed by the curve, the tangent OQ and the line

*x*= 5. [9]