[Math] How to find the equation for a tangent line with a given y intercept.

calculusmultivariable-calculus

So, I have an equation for a circle, $y^2+x^2=3959^2$ and I have the y intercept for a tangent line $y=mx+3965$.
I need to find the equation for the tangent line (the slope)
I have no idea where the first step is, any help would be appreciated.

Best Answer

HINT

Consider the system

  • $y^2+x^2=3959^2$
  • $y=mx+3965$

substitute $y$ in the equation of the circle and, for the quadratic equation obtained, impose that the discriminant is equal to $0$, that is the tangency condition.

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