The correct option is D An ellipse with length of latus rectrum is 2 units
x2+y2=1; x2+2y2=4
Let R(x1,y1) is point of intersection of tangents drawn at P,Q to ellipse ⇒ PQ is chord of contact of R(x1,y1)
⇒xx1+2yy1−4=0
This touches circle ⇒r2(l2+m2)=n2⇒1(x21+4y21)=16⇒x2+4y2=16 is ellipse with eccentricity e=√32 and length of latus rectum LL1=2