There are only two linear functions and that map onto

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

There are only two linear functions

f

and

g

that map

[1,2]

onto

[4,6]

. In a

\triangle ABC

c=f(1)+g(1)

and

a

is the maximum value of

r^2

, where

r

is the distance of a variable point on the curve

x^2+y^2-xy=10

from the origin. Then

\sin a:\sin c

is (1)

1:2

(2)

2:1

(3)

1:1

(4) None of these