A circle has a diameter with endpoints (-7, -1) and (-5, -9).

What is the equation of the circle?

r2 = (x + 6)2 + (y + 5)2
r2 = (x + 4)2 + (y + 1)2
r2 = (x + 6)2 + (y - 1)2
r2 = (x + 4)2 + (y + 5)2

Question

A circle has a diameter with endpoints (-7, -1) and (-5, -9).

What is the equation of the circle?

r2 = (x + 6)2 + (y + 5)2
r2 = (x + 4)2 + (y + 1)2
r2 = (x + 6)2 + (y - 1)2
r2 = (x + 4)2 + (y + 5)2

anonymous · Answer

@ParthKohli

anonymous · Answer

center of the circle is a midpoint of the two given end points. so center of the circle is
$$\left(\frac{-7+-5}{2},\frac{-1+-9}{2}\right) = (-6, -5)$$

anonymous · Answer

that makes sense

anonymous · Answer

Hence equation of the circle is $$(x+6)^2+(y+5)^2=r^2$$

anonymous · Answer

Why does it change from negative to positive?

anonymous · Answer

because the formula is (x - h)^2 + (y - k)^2 = r^2, so when you put negative numbers for h and k, it becomes positive

anonymous · Answer

Ohhh! That makes so much sense! I actually just went over that a few days ago! Can't believe I forgot. Wow! Thanks so much! :)

anonymous · Answer

Glad to help you :D