From any point on the line y=x+4, tangents are drawn to the auxiliary circle of the ellipse x2+4y2=4. If P,Q are the points of contact and A,B are the corresponding points of P and Q on the ellipse respectively, then the locus of the midpoint of AB is

From any point on the line y=x+4, tangents are drawn to the auxiliary

1.	From any point on the line y=x+4, tangents are drawn to the auxiliary circle of the ellipse x2+4y2=4. If P,Q are the points of contact and A,B are the corresponding points of P and Q on the ellipse respectively, then the locus of the midpoint of AB is
Answer» From any point on the line $y = x + 4$ , tangents are drawn to the auxiliary circle of the ellipse $x^{2} + 4 y^{2} = 4.$ If $P, Q$ are the points of contact and $A, B$ are the corresponding points of $P$ and $Q$ on the ellipse respectively, then the locus of the midpoint of $A B$ is