The correct answer is: (x + 2)^2 + (y - 1)^2 = 25
Step-by-step explanation:
Given
Point on circle = P = (-5,-3)
Centre = C = (-2,1)
The distance between C and P is the radius of circle.
So,
[tex]CP = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\= \sqrt{(-5+2)^2+(-3-1)^2}\\=\sqrt{(-3)^2+(-4)^2}\\= \sqrt{9+16}\\=\sqrt{25}\\=5\ units[/tex]
Hence,
r = 5 units
The general form of equation of circle is:
[tex](x-h)^2+(y-k)^2 = r^2[/tex]
Here (h,k) are the coordinates of circle
(h,k) = (-2,1)
Putting the values in standard equation
[tex](x-(-2))^2+(y-1)^2 = (5)^2\\(x+2)^2+(y-1)^2 = 25[/tex]
Hence,
The correct answer is: (x + 2)^2 + (y - 1)^2 = 25
Keywords: Circle, equation of circle
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The equation of the circle will be [tex](x+2)^2+(y-1) = 25\\[/tex]
The formula for calculating the equation of a circle is expressed as:
(x-a)^2+ (y-b)^2= r^2
where:
(a, b) is the center = (-2, 1)
r is the radius
Find the radius
[tex]r=\sqrt{(-3-1)^2+(-5+2)^2} \\r=\sqrt{(-4)^2+(-3)^2}\\ r= \sqrt{16+9}\\ r = 5 units[/tex]
The equation of the circle will be [tex](x+2)^2+(y-1) = 25\\[/tex]
Learn more on equation of a circle here:https://brainly.com/question/1506955
