SOLUTION: Let A be a point on the curve C: x^2 + y^2 - 2x - 4 = 0. If the tangent line to C at A passes through the point P(4, 3) then the length of AP is ____

SOLUTION: Let A be a point on the curve C: x^2 + y^2 - 2x - 4 = 0. If the tangent line to C at A passes through the point P(4, 3) then the length of AP is _____ I've been stumped on this

Question 867556: Let A be a point on the curve C: x^2 + y^2 - 2x - 4 = 0. If the tangent line to C at A passes through the point P(4, 3) then the length of AP is _____
I've been stumped on this for hours, any help would be greatly appreciated. Thank you!
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
You have, or will have, three important points. Point A on the circle; point C the center of the circle (found from standard form after you complete the square) and point P(4,3) off and away from the circle.

You want to solve for y for the equation of the circle, AFTER putting into standard form. You will have a variable coordinate, some unknown (x,y) for A on the circle. y will be some two different functions of x, f(x) and g(x). Your general point then will be (x, f(x)) and (x, g(x)).

Use the fact that, because they are perpendicular, letting m symbolize slope, . Use this to find the value or values of x. Remember, you have two functions to form your circle.

Use x values to find the corresponding y values for point or points "A".

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HELPFUL NOTE: This is a coordinate geometry problem at about the level of Intermediate Algebra. A graph of the situation may be very useful to guide your solution. No differentiation is needed for this exercise. Trying to treat this as a calculus problem will make a solution unnecessarily difficult.
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