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Let $O(0, 0)$ and $A(0, 1)$ be two fixed points. Then the locus of a point $P$ such that the perimeter of $\triangle AOP$ is 4, is:
(1) $8x^2 - 9y^2 + 9y = 18$
(2) $9x^2 - 8y^2 + 8y = 16$
(3) $9x^2 + 8y^2 - 8y = 16$
(4) $8x^2 + 9y^2 - 9y = 18$
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