Answer:
The answer to your question is (x + 3)² + (y + 6)² = 2
Step-by-step explanation:
Endpoints (-4, -7) and (-2, -5)
Process
1.- Find the length of the radius
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
d = [tex]\sqrt{(-2 + 4)^{2}+ (-5 + 7)^{2} }[/tex]
d = [tex]\sqrt{2^{2} + 2^{2} }[/tex]
d = [tex]\sqrt{4 + 4}[/tex]
d = [tex]\sqrt{8}[/tex]
Radius = [tex]\frac{\sqrt{8} }{2}[/tex] = [tex]\sqrt{2}[/tex]
2.- Find the center
Xm = [tex]\frac{-4 - 2}{2} = \frac{-6}{2} = -3[/tex]
Ym = [tex]\frac{-7 - 5}{2} = \frac{-12}{2} = -6[/tex]
Center = (-3, -6)
3.- Write the equation
(x - h)² + (y - k)² = r²
(x + 3)² + (y + 6)² = ([tex]\sqrt{2}[/tex])²
(x + 3)² + (y + 6)² = 2
