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Question

An equation for the line that passes through (10,1) and is perpendicular to y=x242 is

A
4x+y=39
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B
2x+y=19
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C
x+y=9
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D
x+2y=8
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Solution

The correct option is D x+2y=8
Given equation of parabola is
y=x242
dydx=x2
Slope of tangent to parabola at (x1,y1)=x12
Therefore, slope of normal at (x1,y1)=2x1
Also, slope of normal =y1+1x110
y1+1x110=2x1
x1y1+x1=2x1+20
x1y1+3x1=20
Substituting y1=x2184 (from the given equation)
x1(x2184+3)=20
x1(x21+4)=80
x31+4x180=0.
which has one root x1=4
Hence, x1=4;y1=2
P=(4,2)
Therefore, equation of PA is
y+1=12(x10)
2y+2=x+10
x+2y8=0

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