Power of a point tangents Two circles $A$ and $B$ with centers $P$ and $Q$, respectively, are externally tangent to each other. The power of point $P$ with respect to circle $B$ is $8$. The power of point $Q$ with respect to circle $A$ is $15$. What is the ratio of the areas of circle $A$ and circle $B$?

How do I go about solving this problem? Is  there perhaps a formula for ratios of areas of circles given different powers of points?

Power of a point $X$ wrt circle $(O,r)$ is $OX^2-r^2$
Given is $$(a+b)^2-b^2=8 \quad , \quad (a+b)^2-a^2=15$$
Define $x:= a/b$
$$\dfrac{(a+b)^2-a^2}{(a+b)^2-b^2}=\dfrac{15}{8}$$
$$\Rightarrow \dfrac{(x+1)^2-x^2}{(x+1)^2-1^2}=\dfrac{15}{8}$$
$$\Rightarrow x=\dfrac{2}{5}$$
