Question

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

Answer 1

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