Calculus homework

Question

Find the coordinates of all points on the graph of y= 4-x^2 at which the tangent line passes through the point (3,0)

Number of answers:

Answer 1

y' = -2x

Let (a,b) = (a, 4-a^2) = the point of tangency that passes through the point (3,0)

slope = -2a = (4-a^2)/(a-3)

-2a^2 +6a = 4 -a^2

a^2 -6a +4 = 0

a = 6/2 + (1/2)sqr(36-4(4))

a =3 +sqr5 or 3-sqr5

b= 4-a^2 = 4- 9-6sqr5 -5 = -10-6sqr5

or 4 -(3-sqr5)^2 = 4 -(9 -6sqr5 +5) = -10+6sqr5

the points of tangency are (3+sqr5, -10-6sqr5) and (3-sqr5, -10+sqr5)