SOLUTION: The equation of the tangent line to the ellipse x^2/9 +y^2/4=1 at (3/2,3)

Question 652125: The equation of the tangent line to the ellipse x^2/9 +y^2/4=1 at (3/2,3)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The equation of the tangent line to the ellipse
x^2/9 +y^2/4=1 at (3/2,3)
=====================
Take the derivative:
(2/9)x +(1/2)y*y' = 0
---
Solve for y':
y' = [(-2x/9)/(y/2)]
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Evaluate at (3/2,3)
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y' = -3 / (3/2)
----
y' -2
==========
Form: y = mx + b
3 = -2(3/2) + b
3 = -3 + b
b = 5
----
Equation of tangent line:
y = -2x + 5
=================
Cheers,
Stan H.

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