Question

Write an equation for the circle with endpoints of a diameter (9, 4) and (-3, -2)

Answer 1

if the diameter is at (9,4) and (-3,-2), then the center of the circle is the midpoint of that segment.

and since we know that the radius of a circle is half of the diameter, whatever long that diameter segment is, the radius is half that.








`\bf -------------------------------\\\\ \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{1}{ k})\qquad \qquad radius=\stackrel{(√(180))/(2)}{ r} \\\\\\ (x-3)^2+(y-1)^2=\left( (√(180))/(2) \right)^2\implies (x-3)^2+(y-1)^2=\cfrac{(√(180))^2}{2^2} \\\\\\ (x-3)^2+(y-1)^2=\cfrac{180}{4}\implies (x-3)^2+(y-1)^2=45`