Respuesta :
Therefore, the equation of circle is: [tex](x+3)^{2}+(y+5)^{2} = 100[/tex]
What is a circle?
- All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
- The radius of a circle is the separation between any point on the circle and its center.
- The radius must typically be a positive integer. Except when otherwise specified, this article discusses circles in Euclidean geometry, namely the Euclidean plane.
- A circle, specifically, is a straightforward closed curve that separates the plane into its inner and exterior.
Here we know that[tex](h,k) = (-3,5)[/tex]but we are not given the radius.
However, we can find the radius by using the distance formula.
[tex]\sqrt{x^{2} +y^{2} }[/tex], where [tex]x=x_{1} -x_{2}[/tex] and [tex]y=y_{1} -y_{2}[/tex]
Putting the values, we get:
[tex]\sqrt{8^{2} +6^{2} }[/tex]
The radius comes out to be:
[tex]r=10[/tex]
An equation of the circle with center [tex](h,k)[/tex] and radius r is
[tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex]
Now, substituting the values, we get:
[tex](x--3)^{2} +(y-5)^{2} = 10^{2}[/tex]
Therefore, the equation of circle is:
[tex](x+3)^{2}+(y+5)^{2} = 100[/tex]
Know more about circles with the help of the given link:
https://brainly.com/question/10618691
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