# 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)

#### Solution:

$x_{0}=1 \ \\ y_{0}=20 \ \\ \ \\ 8x+5y-19=0 \ \\ \ \\ s=8 \cdot \ x_{0}+5 \cdot \ y_{0}-19=8 \cdot \ 1+5 \cdot \ 20-19=89 \ \\ a=\sqrt{ 8^2+5^2 }=\sqrt{ 89 } \doteq 9.434 \ \\ r=\dfrac{ s }{ a }=\dfrac{ 89 }{ 9.434 } \doteq \sqrt{ 89 } \doteq 9.434 \ \\ \ \\ (x-x_{0})^2 + (y-y_{0})^2=r^2 \ \\ e=(x-1)^2+(y-20)^2=89$

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Showing 1 comment:
Dr Math
Hint - use formula for Distance Between a Point and a Line = which is radius of circle

2 years ago  2 Likes

Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Pythagorean theorem is the base for the right triangle calculator.

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