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a circle has a center located at 2 5 and passes through the point 10 3 answer
Determine the equation of the circle. Show how you arrived at your answer.
Write the equation of the tangent line to the circle at the point . Show how you determined your answer.

Respuesta :

Answer:

[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]

Step-by-step explanation:

Givens

  • The center of the circle is at (2,5).
  • A point on the circumference is at (10,3).

First, we need to find the radius, which is the distance between the given points.

[tex]d=\sqrt{(3-5)^{2} +(10-2)^{2} } =\sqrt{4+64}=\sqrt{68}[/tex]

Therefore, the radius of the circle is

[tex]r \approx 8.25[/tex]

The explicit form of the equation of the circle would be

[tex](x-2)^{2} +(y-5)^{2} =\sqrt{68}[/tex]

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