Question

Let A be a point on the Curve C: x²+y² -2x - 4 =0. If the tangent line to C at A passes through P(4,3), then the lenght of AP is:

Answer 1

By implicit differentiation, 2yy' +2x -2 = 0, 2yy' = -2x + 2, y'=-2x+2/y.

Answer 2

I can find its inclination... but then what?

Answer 3

wth is calculus required ?

Answer 4

Its a calculus exercise, so I suppose that it does.

Answer 5

you know the inclination, you know a poit P(4, 3) so you have the equation of tangent

Answer 6

The general case, yeah. But I need to find the point A in order to find the inclination of the line. My other problem is with typical curves, such as the circle equations :P

Answer 7

y' would be -2x+2/sqrt(-x²+2x+4)

Answer 8

Which is the inclination

Answer 9

By using tcarroll010's tips, I found C's radius, which is sqrt(5).
The distance between O (C's center point) and P is given by\[dOP=\sqrt{(1-4)² + (0+3)²}=3\sqrt{2}.\] Given R and dOP, I can find the distance AO and AP by using the Pythagorean theorem