length of tangent to a curve passing through another point Let $A$ be a point on the curve

$\mathcal{C} : x^2+y^2-2x-4=0$

If the tangent line to $\mathcal{C}$ at $A$ passes through $P(4,3)$, then what is the length of AP?
Please, include a general method of approaching similar kind of questions.

Bring the circle into standard form to find our center location and radius.
$$ ( h,k)=(1,0),\, R = \sqrt5 = CT $$
Distance of center to outside point squared
$$ PC^2 = (4-1)^2+ (3-0)^2= 18 $$
$$ PT^2= PC^2-5 = 18-5= 13 \rightarrow PT= \sqrt{13} $$

