x²/3 + y²/3 = 4
start by multiplying everything by 3 to get rid of fractions
x² + y² = 12
(it's a circle)
take derivative with respect to x
2x + 2yy' = 0
solve for y' now
2x = -2yy'
2x/(-2y) = y'
-x/y = y'
use the given point (-33,1)
-(-33)/1 = y'
y' = 33
y' is rate of change or slope at that point. Now you can use the point (-33,1) again to find y-intercept "b" for the tangent line.
Line so far:
y = 33x + b
plug in (-33,1)
1 = 33(-33) + b
1 = -1089 + b
1090 = b
tangent line is:
y = 33x + 1090
