Question

(Score for Question 2:__ of 5 points

Answer 1

The general equation of a given circle is $x^{2} +y^{2} +2x+6y+9=0$

Given a plot of the circle in the X-Y plane, The center of circle has the coordinates  ( -1, -1) and the circle is passing through (-1 ,-4) and (-1 ,-2)  and  (-1 ,-4)  , (-1 ,-2)   are coordinates of diametrically opposite ends of circle

If there are two points on a circle (x₁, y₁) and (x₂, y₂) that are at opposite ends of the same diameter, then the circle's equation can be written as

(x-x₁)(x-x₂)+(y-y₁)(y-y₂)=0

Given x₁= -1 , x₂ = -1  ,  y₁= -4 , y₂= -2

The circle's equation can be written as ( x+1)(x+1) + (y+4)(y+2)

⇒$x^{2} +1+2x+y^{2} +6y+8=0$

⇒$x^{2} +y^{2} +2x+6y+9=0$

Therefore, $x^{2} +y^{2} +2x+6y+9=0$ is the general equation of circle.

Hence,The general equation of a given circle is $x^{2} +y^{2} +2x+6y+9=0$

Learn more about circle here:

brainly.com/question/11833983

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