Determine the coordinates of two points of tangency to the curve y=-2x^2, given that the corresponding tangent lines intersect at point (2,8). Can someone please tell me what the answer is? and what the approach it took

Question

anonymous · Answer

a point on the curve looks like $(x,-2x^2)$ and if the tangent line passes through $(2,8)$ it will have slope 
$$\frac{-2x^2-8}{x-2}$$

anonymous · Answer

it will also have the same slope as the derivative at that point, and the derivative is $-4x$ meaning you have an equation 
$$\frac{-2x^2-8}{x-2}=-4x$$ which you can solve for $x$

anonymous · Answer

probably easiest to start by multiplying both sides by $-1$ and solving 
$$\frac{2x^2+8}{x-2}=4x$$

anonymous · Answer

pretty clear that you are going to get a quadratic equation to solve, which is why there will be two solutions

buggiethebug · Answer

wait can you tell me what the answers are, i have no clue, and there isn't a way to check

buggiethebug · Answer

we didnt learn derivatives...

buggiethebug · Answer

are the x values 2+/-2sqrt(2) ?

anonymous · Answer

you can't possibly do this problem without derivatives
at least no way that i can think of

anonymous · Answer

yes you have the right answers, 
$$x=2\pm\sqrt{2}$$