# Math Help - Calculus slope intersection

1. ## Calculus slope intersection

Can someone show me how to find the points that intersect with the graph of the function f(x) = 1-x^2 and the tangent line that goes through the point (2,0).

2. Originally Posted by pantera
Can someone show me how to find the points that intersect with the graph of the function f(x) = 1-x^2 and the tangent line that goes through the point (2,0).
The point is on the curve $f(x)=1-x^2$. Say the point is $(a,1-a^2)$. The slope of the tangent line is $k=f'(a)=-2a$. So the tangent line is
$f(x)=-2a(x-a)+1-a^2=-2ax+1+a^2$
The line passes through the point $(2,0)$, then $0=-4a+1+a^2$
Therefore, $a= 2\pm\sqrt{3}$

3. Thank you so much!