關於微積分的應用的一條問題.

設該兩條切線與曲線切於(a, b)
9x^2 + 16y^2 = 52
18x + 32y*dy/dx = 0
dy/dx = -9x/16y
dy/dx |(a, b) = -9a/16b
所需切線的斜率 = 9/8
-9a/16b = 9/8
-a/2b = 1
a = -2b
而且, 9a^2 + 16b^2 = 52
9(-2b)^2 + 16b^2 = 52
52b^2 = 52
b = 1 或 -1
當b = 1, a = -2, 切線方程: y-1 = (9/8)(x+2), i.e. 9x-8y+26 = 0
當b = -1, a = 2, 切線方程: y+2 = (9/8)(x-2), i.e. 9x-8y-26 = 0