4. Given two circles $C_{1}: x^{2}+y^{2}=1$ and $C_{2}$ : $(x-2)^{2}+y^{2}=16$. Then the locus of the center of the circle that is externally tangent to $C_{1}$ and internally tangent to $C_{2}$ is $\qquad$
$\qquad$
4. $\frac{(x-1)^{2}}{\frac{25}{4}}+\frac{y^{2}}{\frac{21}{4}}=1$