Well the origin is always (0,0) so any graph that passes it has to go through that point!
Maybe you read the question incorrectly.
It always helps to know the original question, rather than a (wrong) interpretation of the original question.
The tangent to the curve y = 1/x^2+8x+16 passing through the origin is very different to y = 1/x^2+8x+16 passing through the origin. Even though y = 1/x^2+8x+16 is completely ambiguous (is it 1/(x^2+8x+16) or (1/x^2) + 8x + 16 .....?) none of the possible interpretations of the equation of your curve pass through the origin.
Please be clearer what the equation of the curve is.