Question

Complete the equation for ⊙A.

Answer 1

The general equation of a circle is (x-h)²+(y-k)² = r². The equation of circle A is (x+4)²+(y+2)²=9.

What is the equation of a circle?

The general equation of a circle is given as,

(x-h)²+(y-k)² = r²

Where (h,k) is the coordinate of the centre of the circle, and r is the radius of the circle,

Given that the four points that lie on the circle are  (-4,1), (-1,-2), (-4, -5) and (-7,-2), and also the centre of the circle is at (-4,-2). Therefore, the radius of the circle will be the distance between the centre of the circle and any point lying on the circle.

$\rm \text{Radius of the circle} = \sqrt{[(-4)-(-4)]^2+[(-2)-(1)]^2}\\\\\text{Radius of the circle} = \sqrt{(0)^2+(-3)^2}\\\\\text{Radius of the circle} = 3\ units$

Since the coordinate of the centre point of the circle is (-4,-2), while the radius of the circle is 3 units, therefore, the equation of the circle can be written as,

$[x-(-4)]^2+[y-(-2)]^2 = 3^2\\\\(x+4)^2+(y+2)^2 = 3^2\\\\(x+4)^2+(y+2)^2 = 9$

Hence, the equation of circle A is (x+4)²+(y+2)²=9.

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