Find the Pairs (X, Y) That Give the Extreme Values $4 x ^ { 2 } + 5 y ^ { 2 } = 8400$

Short Answer

Find the pairs (x, y) that give the extreme values of 2x + 10y, subject to the constraint $4 x ^ { 2 } + 5 y ^ { 2 } = 8400$ using the method of Lagrange multipliers.
Enter your answer as exactly just (a, b), (c, d) where a > c (no words).