Question

Find an equation of the circle whose diameter has endpoints (-4,-6) and (-6, 4). ​

Answer 1

`(x+5)^2+(y+1)^2=104.`

Explanation:

1) the equation of the circle is: (x-x₀)²+(y-y₀)²=r², where point(x₀;y₀) - centre of the circle, r - radius of the circle.

2) the coordinates of the centre are:

`x_0=(-4-6)/(2) =-5;`

`y_0=(4-6)/(2)=-1;`

3) the radius is the distance between (-5;-1) and (-4;-6):

`r^2=√((-4+6)^2+(-6-4)^2)=√(104);`

4) finally, the required equation is:

(x+5)²+(y+1)²=(√104)².