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
[tex]\sqrt{(2-(-4))^{2}+(3-5)^{2}}[/tex] = 2[tex]\sqrt{10}[/tex]
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 ([tex]\frac{2-4}{2},\frac{3+5}{2}) =(-1, 4)[/tex]
Therefore the equation of the circle is
(x+1)² + (y-4)² = (√10)²
⇒ (x+1)² + (y-4)² = 10 (Answer)
