Find equations of all lines tangent to y=9-x^2 that pass through the point (1,12).

Question

hero · Answer

This can be done without calculus right? @satellite73

anonymous · Answer

i don't think so

hero · Answer

Okay @iloveme17. You seem to already know how to do it. What is the difficulty here?

anonymous · Answer

how do i seem to know how to do it i have no idea how to ...

anonymous · Answer

ok, you know the derivative is $-2x$ right? and any point on the curve looks like 
$(x,9-x^2)$ 
the slope between that general point and the specific point $(1,12)$ will be 
$$m=\frac{9-x^2-12}{x-1}$$ and that must be equal to $-2x$

anonymous · Answer

so your job is to set 
$$\frac{9-x^2-12}{x-1}=-2x$$
$$\frac{-3-x^2}{x-1}=-2x$$ etc 
it is a quadratic , that is why you get two answers

anonymous · Answer

@hero i am not sure of how you can do this without using calc, mainly because the notion of a tangent line is a calc idea.  that is not to say there isn't some other way

anonymous · Answer

thank you

anonymous · Answer

yw
i take it you are good from there