Find the 5

Find the equation with center at (1,20) which touches the line 8x+5y-19=0

Result

e = (Correct answer is: e = pow(x-1, 2)+pow(y-20, 2) = 89) Wrong answer

Solution:

x0=1 y0=20  8x+5y−19=0  s=8⋅ x0+5⋅ y0−19=8⋅ 1+5⋅ 20−19=89 a=82+52=89≐9.434 r=sa=899.434≐89≐9.434  (x−x0)2+(y−y0)2=r2 e=(x−1)2+(y−20)2=89x_{0}=1 \ \\ y_{0}=20 \ \\ \ \\ 8x+5y-19=0 \ \\ \ \\ s=8 \cdot \ x_{0}+5 \cdot \ y_{0}-19=8 \cdot \ 1+5 \cdot \ 20-19=89 \ \\ a=\sqrt{ 8^2+5^2 }=\sqrt{ 89 } \doteq 9.434 \ \\ r=\dfrac{ s }{ a }=\dfrac{ 89 }{ 9.434 } \doteq \sqrt{ 89 } \doteq 9.434 \ \\ \ \\ (x-x_{0})^2 + (y-y_{0})^2=r^2 \ \\ e=(x-1)^2+(y-20)^2=89

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Dr Math
Hint - use formula for Distance Between a Point and a Line = which is radius of circle

2 years ago  2 Likes
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