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**ameerulislam** Q: Find the coordinates of all points on the graph of $\displaystyle y=1-x^2$ at which the tangent line passes through the point $\displaystyle (2,0)$

__My solution so far:__

What I understood is that there is a point on outside the parabola/ curve $\displaystyle (2,0)$ and another point is on the curve which is unknown and need to figure out $\displaystyle (x, y)$ and they are connected through a tangent line.

Now first let me figure out the derivative/slope of the tangent line over that curve.

$\displaystyle y=1-x^2$

$\displaystyle f(x)=1-x^2$ { is y always equals f(x)? maybe this is only when y is function of x right?}

$\displaystyle f'(x)=-2x$

So now we know the slope of the tangent line

we know 2 co-ordinates of one end $\displaystyle (2,0)$ and need to figure out the other end $\displaystyle (x,y)$.

and we can use the slope formula here

$\displaystyle \frac{0-y}{2-x}=-2x$

$\displaystyle x=2\pm2\sqrt{3}$ **CORRECT**