Tangent Line and Circle

Question

Find the values of c such that the line with equation y=2x+c is a tangent to the circle with equation x^2+y^2=25.

Answer 1

take the derivative of the circle equation to get

2xx' + 2yy' = 0

y'/x' = -x/y = 2 = slope

y= -x/2

substitute that into the circle equation and solve for x

x^2 + (-x/2)^2 = 25

x= + or - 2sqr5

= about + or - 4.4

y =2x + 3 = 2(+ or - 4.4) + 3 = 8.8+ 3 or -8.8 + 3 = 11.8 or -5.8