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2. Find the equation of the tangent line to the parabola y = x² – 8x+9 at the point (3, –6)

2. Find the equation of the tangent line to the parabola y = x² – 8x+9 at the point (3, –6)

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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2. Find the equation of the tangent line to the parabola y = x² – 8x +9 at the point (3, –6)
Transcribed Image Text:2. Find the equation of the tangent line to the parabola y = x² – 8x +9 at the point (3, –6)
Expert Solution
Step 1

Given

y=x2-8x+9

Formula:

dydx(xn)=nxn-1

dydx(k)=0, where k is a constant

Consider

y=x2-8x+9

Differentiating with respect to x,

dydx=2x-8

dydx(3,-6)=2(3)-8=6-8

dydx(3,-6)=-2=m

Now the equation of the tangent at (x1, y1) is

y-y1=m x-x1

Equation of the tangent at the point (3, -6) is

y-(-6)=-2x-3

y+6=-2x+6

y+2x=0

2x+y=0

y=-2x

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