<s>[INST] How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$ Problem : 
How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$ 
My working on this : 
Two lines are perpendicular if the sum of coefficient of $x^2$ and $y^2$ is equal to zero. 
 [/INST] HINT:
$$3y^2-y(x+1)+2x-10=0$$
$$y=\frac{x+1\pm\sqrt{(x+1)^2-12(2x-10)}}{2\cdot3}=\frac{x+1\pm\sqrt{x^2-22x+121}}6=\frac{x+1\pm(x-11)}6$$
Can you determine the gradients from here and reach the destination?
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