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The tangent to a curve intersects x axis at $B$ and $y$ at $A$. The normal to same curve intersects $x$ axis at $C$ and $Y$ axis at $D$. Given $\large\frac{AO}{OB}= \frac{OC}{CD}$ curve passes through $(2,3)$. Find the curve

$(a)\;y^2=-x^3+9x^2+t \\(b)\;y^2=-x^4+\frac{25}{4}x^2 \\ (c)\;y^2=-2x^4+25x^2 \\ (d)\;y^2=-2x^2+3x^3 $

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