Question

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 1

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 = $\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }$

   d = $\sqrt{(-2 + 4)^{2}+ (-5 + 7)^{2} }$

   d = $\sqrt{2^{2} + 2^{2} }$

   d = $\sqrt{4 + 4}$

   d = $\sqrt{8}$

   Radius = $\frac{\sqrt{8} }{2}$ = $\sqrt{2}$

2.- Find the center

Xm = $\frac{-4 - 2}{2} = \frac{-6}{2} = -3$

Ym = $\frac{-7 - 5}{2} = \frac{-12}{2} = -6$

Center = (-3, -6)

3.- Write the equation

                                   (x - h)² + (y - k)² = r²

                                   (x + 3)² + (y + 6)² = ($\sqrt{2}$)²

                                   (x + 3)² + (y + 6)² = 2