Implicit Differentiation
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Implicit Differentiation

[From: ] [author: ] [Date: 12-03-20] [Hit: ]
(a) At what two points is x = 4?(b) Find the equation of the tangent line to the circle at Point A.(c) Find the equation of the tangent line to the circle at Point B.(c)Find the equation of the normal line to this circle at Point A.(d) Find the equation of the normal line to this circle at Point B.(e) At what point do the two normal lines intersect?......
I have no idea how to approach this problem, ANY help is appreciated. Thanks!
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You are given the circle, x^2 + y^2 = 25.

(a) At what two points is x = 4?


(b) Find the equation of the tangent line to the circle at Point A.


(c) Find the equation of the tangent line to the circle at Point B.



(c) Find the equation of the normal line to this circle at Point A.



(d) Find the equation of the normal line to this circle at Point B.



(e) At what point do the two normal lines intersect?

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When x=4 we can have y = 3 or y = -3.

For the slopes use implicit differentiation:

x^2 + y^2 = 25
2xdx + 2ydy = 0

Thus dy/dx = -x/y, which allows you to compute the tangent line's slope at any point on the circle. Normal lines will have slope of the negative reciprocal of this, i.e., y/x.
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