Question

Find all points (a,f(a)) on the graph of f(x)=x^2 where the line tangent to the graph of y=f(x) goes through the point (2,-5).

Answer 1

just did one almost identical to this one
points on the graph look like \((x,x^2)\) and slope between this arbitrary point and \((2,-5)\) is
\[\frac{x^2+5}{x-2}\] you also know the slope is given by \(2x\) the derivative, so you job is to set
\[\frac{x^2+5}{x-2}=2x\] and solve the resulting quadratic equation for \(x\)