SOLUTION: Find the equation of the normal to y=(2x-1)(3x+5) at the point (1,8). Give your answer in the form ax+by+c=0,where a,b and c are integers

Algebra ->  Rational-functions -> SOLUTION: Find the equation of the normal to y=(2x-1)(3x+5) at the point (1,8). Give your answer in the form ax+by+c=0,where a,b and c are integers      Log On


   

Question 880836: Find the equation of the normal to y=(2x-1)(3x+5) at the point (1,8). Give your answer in the form ax+by+c=0,where a,b and c are integers
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the derivative of the function at that point.
The value of the derivative is the slope of the tangent line at that point.
Tangent and normal lines are perpendicular to each other.
Determine the slope of the normal line from the tangent line slope.
Use the point slope form to determine the equation of the normal line.
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y=%282x-1%29%283x%2B5%29
y=6x%5E2%2B7x-5
dy%2Fdx=12x%2B7
At x=1,
m%5BT%5D=dy%2Fdx=12%281%29%2B7
m%5BT%5D=19
Perpendicular lines have slopes that are negative reciprocals,
m%5BT%5D%2Am%5BN%5D=-1
19%2Am%5BN%5D=-1
m%5BN%5D=-1%2F19
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When x=1, y=%282-1%29%283%2B5%29=8
y-8=-%281%2F19%29%28x-1%29
y-8=-%281%2F19%29x%2B1%2F19
y-8=-%281%2F19%29x%2B1%2F19
y=-%281%2F19%29x%2B1%2F19%2B152%2F19
y=-%281%2F19%29x%2B153%2F19
19y=-x%2B153
x%2B19y-153=0
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