A circle has center at (7, 0). What is the equation of the line that is tangent to the circle at (2, 0) ?

First find equation

center is (h, k) then

(x-h) ^2 + (y-k) ^2=r^2

given

(7,0) is center

(x-7) ^2+y^2=r^2

also given (2,0)

(2-7) ^2+0^2=r^2

(-5) ^2=r^2

25=r^2

(x-7) ^2+y^2=25 is equation

take derivitive of both sides, implicit differntiaton

2 (x-7) + 2y dy/dx=0

2 (x-7) = - 2y dy/dx

(7-x) / y=dy/dx

at (2,0)

(7-2) / 0

undefined

that means the line is x=something

(2,0)

the equation is x=2