Find curve in $x-y$ plane which passes through$(1,1)$ . Intersects line $y=x$ at right angle at that point and satisfies $xy''+2y''=0$

Question

$(a)\;y=\frac{1}{x^2} \\ (b)\;y = \frac{1}{x} \\ (c)\;y=0 \\ (d)\;y=x^2$