Write the equation of the line tangent to the curve

x^2 − 4y^2 + 192 = 0 at (8, 8)
Thank You

x^2 - 4y^2 + 1292 = 0

2x - 8yy' = 0
y' = x/4y

You have x and y, so y' = 1/4

the line is thus

y-8 = 1/4 (x-8)

see at

http://www.wolframalpha.com/input/?i=plot+x%5E2+%E2%88%92+4y%5E2+%2B+192+%3D+0%2C+y+%3D+1%2F4+%28x-8%29%2B8