Question

A circle has a diameter with endpoints (-10, -6) and (-2, -4).

What is the equation of the circle?

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

Answer 1

Answer: $(x+6)^{2}+(y+5)^{2}=r^{2}$

Step-by-step explanation:

The formula for finding the equation of circle with center (a,b) is given as :

$(x-a)^{2}+(y-b)^{2}=r^{2}$

The end point of the diameter is given as :

(-10, -6) and (-2, -4) , this means that the coordinate of the center is the Mid -point of the end point .

The mid - point = ( -6 , - 5)

substituting into the formula , we have

$(x-(-6))^{2}+(y-(-5))^{2}$$= r^{2}$

$(x+6)^{2}+(y+5)^{2}=r^{2}$

This is the equation of the circle