Find the 5

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

Result

e = (Correct answer is: )

Step-by-step explanation:

$$\begin{gathered} x_0=1 \\ {y}_0=20 \\ 8x+5y-19=0 \\ s=8\cdot x_0+5\cdot y_0-19=8\cdot 1+5\cdot 20-19=89 \\ a=\sqrt{8^2+5^2}=\sqrt{89}\doteq 9.434 \\ r={\displaystyle \frac{s}{a}}={\displaystyle \frac{89}{9.434}}=\sqrt{89}\doteq 9.434 \\ (x-x_0{)}^2+(y-y_0{)}^2=r^2 \\ e:(x-1{)}^2+(y-20{)}^2=89 \end{gathered}$$

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Dr Math

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

3 years ago  2 Likes Like

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