Question

write an equation for a circle with a diameter that has endpoints at (8 7) and (-4 -3)

Answer 1

First find the midpoint, which will also be our center.
\[(\frac{ -4+8 }{ 2 },\frac{ -3+7 }{ 2 })\]
= (2, 2)

Now to find the radius.
Using the distance formula from our vertex to one of the endpoints.
\[r=\sqrt{(8-2)^{2}+(7-2)^{2}}=\sqrt{36+25}=\sqrt{61}\]

Equation of circle: r^2=(x-h)^2+(y-k)^2 where (h,k) is the center, so
\[61=(x-2)^{2}+(y-2)^{2}\]

Answer 2

brusmack gave the correct answer. There is other alternate method for this question. As we know that if we take any point on a circle and join this point to the two end points as given diameter then the angle formed is a right angle and we can apply Pythagoras theorem like
(\[\sqrt{(x-8)^{2}+(y-7)^{2}}+\sqrt{(x+4)^{2}+(y+3)^{2}}=\sqrt{(8+4)^{2}+(7+3)^{2}}\]