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For problems 1 through 6 , write the equations of the tangent and normal at the given point. $x^2+y^2=25$ at $(3,4)$

   For problems 1 through 6 , write the equations of the tangent and normal at the given point.
$x^2+y^2=25$ at $(3,4)$
Technical Mathematics with Calculus
Technical Mathematics with Calculus
Paul A. Calter;… 3rd Edition
Chapter 28, Problem 5 ↓
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For problems 1 through 6 , write the equations of the tangent and normal at the given point. $x^2+y^2=25$ at $(3,4)$
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Transcript

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00:01 To solve this problem, first we have to understand the equation of the tangent line.
00:08 Equation of the tangent line is equal to y is equal to m into x minus x1 plus y1.
00:16 So x1 and y1 is the point on the line and m is equal to d y by d x.
00:24 That means the derivative of y.
00:27 So let's see how we'll compute.
00:29 First we have to find from this equation derivative of y with respect to x.
00:37 We have also given point minus 3 and 2.
00:45 So we can write also here minus 3 and 4.
00:55 First we will compute the derivative.
00:57 So take the derivative of given equation with respect to x.
01:02 So we can get d by d x x x into x squared plus.
01:07 D by d x into y square is equal to d by d x into 205 as you know the derivative of x square we can write 2 into x and 2 y here we have to apply the channel so we can write derivative of y squared into 2y also we have to write y by d x because here is the function of y with respect to so we have to write after derivative we can write the d -x as you know the derivative of constant term is equal to 0...
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