Correct option is (3) (2, ±\(\frac 32\))
\(\therefore\) given circle are touching internally
Let a variable circle with centre P and radius r
⇒ PA = r1 – r and PB = r2 + r
⇒ PA + PB = r1 + r2
⇒ PA + PB = 4 ( > AB)
⇒ Locus of P is an ellipse with foci at A(0, 0) and B(2, 0) and length of major axis is 2a = 4, e = \(\frac 12\)
⇒ centre is at (1, 0) and b2 = a2(1 – e2) = 3 if x-ellipse
⇒ E : \(\frac{(x-1)^2}4+\frac{y^2}3\) = 1
which is satisfied by \((2,±\frac 32)\)