write an equation for a circle with a diameter that has endpoints at (-4, -7) and (-2, -5). round to the nearest tenth if necessary.

Answer:The answer to your question is          (x + 3)² + (y + 6)² = 2Step-by-step explanation:Endpoints (-4, -7) and (-2, -5)Process1.- 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 centerXm = [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