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`4a^(2)` sq. units`(8a^(2))/(15)` sq. units`(16a^(2))/(9)` sq. unitsNone of these

Answer :

BSolution :

`ay^(2)=x^(2)(a-x)or y=pm xsqrt((a-x)/(a))` <br> `"Curve tracing : "y=xsqrt((a-x)/(a))` <br> We must have `xlea` <br> `"For "0ltxlea, ygt0 and" for "xlt0, ylt0` <br> `"Also "y=0rArrx=0,a` <br> Curve is symmetrical about x-axis. <br> `"When "xrarr-oo,yrarr-oo` <br> Also, it can be verified that y has only one point of maxima for `0ltxlta.` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_CAL_C09_E04_030_S01.png" width="80%"> <br> `"Area "=2overset(a)underset(0)intxsqrt((a-x)/(a))dx` <br> `sqrt((a-x)/(a))=t` <br> `rArr" "1-(x)/(a)=t^(2)or x=a (1-t^(2))` <br> `rArr" "A=2overset(0)underset(1)inta(1-t^(2))t(-2at)dt` <br> `4a^(2)overset(1)underset(0)int(t^(2)-t^(4))dt` <br> `=4a^(2)[(t^(3))/(3)-(t^(5))/(5)]_(0)^(1)` <br> `=4a^(2)[(1)/(3)-(1)/(5)]` <br> `=(8a^(2))/(15)` sq. units.