Question

Find an equation of the circle whose diameter has endpoints (2,3) and (-4,5)

Answer 1

Answer:

(x+1)² + (y-4)² = 10

Step-by-step explanation:

The diameter of a circle has the endpoints at (2,3) and (-4,5).

Therefore, the length of the diameter is given by

$\sqrt{(2-(-4))^{2}+(3-5)^{2}}$ = 2$\sqrt{10}$

Hence, the radius of the circle is √10.

Now the midpoint of the line joining (2,3) and (-4,5) will be the center of the straight line.

Hence, the center will be at ($\frac{2-4}{2},\frac{3+5}{2}) =(-1, 4)$

Therefore the equation of the circle is  

(x+1)² + (y-4)² = (√10)²

⇒  (x+1)² + (y-4)² = 10 (Answer)