Respuesta :
Answer:
[tex](x - 2)^{2} + (y - 3)^{2} = 36[/tex] is the equation of the circle
Step-by-step explanation:
[tex](x - h)^{2} + (y - k)^{2} = r^{2}[/tex] where (h, k) is the center and r is the radius
In this case h = 2 and k = 3 and r = 6 (see below)
r adius =
[tex]\sqrt{(2 + 3)^{2} + (3 - 6)^{2} } \\= \sqrt{5^{2} + (-3)^{2} } \\= \sqrt{25 + 9\\}\\ = \sqrt{36} = 6[/tex]
Therefore, [tex](x - 2)^{2} + (y - 3)^{2} = 36[/tex] is the equation of the circle
The point (- 3, 6) is on a circle with a center at (2, 3) So, the equation of the circle will be (x-2)^{2} +(y-3)^{2}= 6^{2}.
What is the general equation of a circle?
The general equation of a circle of radius represents all the points that lie on the circumference of the given circle.
The general equation of a circle is:
[tex]\rm (x-h)^{2} +(y-k)^{2}= r^{2}[/tex]
where (h, k) is the center and r is the radius
The point (- 3, 6) is on a circle with a center at (2, 3).
here, h = 2 and k = 3
[tex]\sqrt{(2+3)^{2} +(3-6)^{2}} \\\\\sqrt{5^2+3^2} \\\\\sqrt{36} \\\\6[/tex]
therefore, the radius is 6 units.
Now, the equation of a circle is:
[tex]\rm (x-h)^{2} +(y-k)^{2}= r^{2}[/tex]
[tex]\rm (x-2)^{2} +(y-3)^{2}= 6^{2}[/tex]
Learn more about the equation of a circle;
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