find the standard form of a circle with a diameter that has endpoints (-4,8) amd (9,-6)

Question

hero · Answer

Find the midpoint of the diameter

anonymous · Answer

How do I do that?

sabrina1 · Answer

thanks:)

anonymous · Answer

the midpoint of the diameter is the center$$x _{m}=.5(9-4)=5/2$$$$y _{m}=.5(8-6)=1$$the center of the circle is (5/2, 1)

anonymous · Answer

the circle follows the form$$(x-h)^2+(y-k)^2=r^2$$and we just found h and k so$$(x-5/2)^2+(y-1)^2=r^2$$now we just need to find the radius, or easier is the radius squared

sabrina1 · Answer

yes radius is squared

sabrina1 · Answer

should we just put in the diameter coordinates in equation of the circle and then solve to find radius?

anonymous · Answer

the radius is the distance from the center to either of the given points; i choose to use (-4,8); formula is $$r^2=(5/2-(-4))^2+(1-8)^2=\frac{169}{4}+49=\frac{365}{4}$$

anonymous · Answer

putting it all together$$(x-5/2)^2+(y-1)^2=\frac{365}{4}$$assuming i didn't make any arithmetic errors!