The value of a for the ellipse x2a2+y2b2=1,(a>b) if the extremities of the latusrectum of the ellipse having positiveordinates lie on the parabola x2=−2(y−2) is

±ae,b2a are extremities of the latusrectum having positive ordinates. Then,a2e2=−2b2a−2----1But  b2=a21−e2----2Therefore, from (1) and (2), we geta2e2−2ae2+2a−4=0or  ae2(a−2)+2(a−2)=0∴ae2+2(a−2)=0Hence, a=2.