Question

Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?

Answer 1

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,

$CP = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\= \sqrt{(-5+2)^2+(-3-1)^2}\\=\sqrt{(-3)^2+(-4)^2}\\= \sqrt{9+16}\\=\sqrt{25}\\=5\ units$

Hence,

r = 5 units

The general form of equation of circle is:

$(x-h)^2+(y-k)^2 = r^2$

Here (h,k) are the coordinates of circle

(h,k) = (-2,1)

Putting the values in standard equation

$(x-(-2))^2+(y-1)^2 = (5)^2\\(x+2)^2+(y-1)^2 = 25$

Hence,

The correct answer is: (x + 2)^2 + (y - 1)^2 = 25

Keywords: Circle, equation of circle

Learn more about equation of circle at:

• brainly.com/question/9231234
• brainly.com/question/9214411

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