/Find the equation of tangent and normal line for the following: 1 f(x)=2x2-7,(2,1) Sol. y=8x-15 , X+8y-103D0 2 f(x)=5+2x-x2 , (0,5) Sol. y=2x+5 , X+2y=10 f(x)=x2+x+1 , (1,3) Sol. y=3x , X+3y-103D0 3

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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/Find the equation of tangent and normal line for the following:
f(x)=2x2-7 , (2,1)
Sol. y=8x-15 ,x+8y-10=O
2
f(x)=5+2x-x2 , (0,5)
Sol. y=2x+5 , x+2y=10
3
f(x)=x²+x+1 ,(1,3)
Sol. y=3x , X+3y-10=0
-1
4
x²+xy+2y2=28 , (2,3)
Sol. y=x+4 , y=2x-1
5 F(x) =Vx , (8,2)
Sol. x-12y+16=0 , 12x+y=98
3
f(x)=V4-x , (0,3)
Sol. y=0,
» X=0
7 y=x3 -8x2+9X+20 , (4,-8)
Sol. y=-7x+20 ,x-7y=60
x2-1
8 f(x)='
,(1,0)
Sol. y=x-1 , y31-x
x2+1
V2x+/3y=5, (2,3)
Sol. y=-X+5
, y3x+1
Q 4/Find the points where the tangent line to the graph of f(x)=D2VR and
(1,2) crosses (a) the x-axis and (b) the y-axis
Sol. (-1,0) (0,1)
Transcribed Image Text:/Find the equation of tangent and normal line for the following: f(x)=2x2-7 , (2,1) Sol. y=8x-15 ,x+8y-10=O 2 f(x)=5+2x-x2 , (0,5) Sol. y=2x+5 , x+2y=10 3 f(x)=x²+x+1 ,(1,3) Sol. y=3x , X+3y-10=0 -1 4 x²+xy+2y2=28 , (2,3) Sol. y=x+4 , y=2x-1 5 F(x) =Vx , (8,2) Sol. x-12y+16=0 , 12x+y=98 3 f(x)=V4-x , (0,3) Sol. y=0, » X=0 7 y=x3 -8x2+9X+20 , (4,-8) Sol. y=-7x+20 ,x-7y=60 x2-1 8 f(x)=' ,(1,0) Sol. y=x-1 , y31-x x2+1 V2x+/3y=5, (2,3) Sol. y=-X+5 , y3x+1 Q 4/Find the points where the tangent line to the graph of f(x)=D2VR and (1,2) crosses (a) the x-axis and (b) the y-axis Sol. (-1,0) (0,1)
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