Answer:
The answer to your question is ( x - 2)² + (y + 1)² = 34
Step-by-step explanation:
Data
(7, -4)
(-3, 2)
Process
1.- Calculate the radius of the circle
Formula
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
Substitution
d = [tex]\sqrt{(-3 - 7)^{2} + (2 + 4)^{2}}[/tex]
Simplification
d = [tex]\sqrt{(-10)^{2} + (6)^{2}}[/tex]
d = [tex]\sqrt{100 + 36}[/tex]
d = [tex]\sqrt{136}[/tex] = [tex]2\sqrt{34}[/tex]
radius = [tex]\sqrt{34} / 2[/tex]
radius = [tex]\sqrt{34}[/tex]
- Find the center
Xm = [tex]\frac{7 - 3}{2} = \frac{4}{2} = 2[/tex]
Ym = [tex]\frac{-4 + 2}{2} = \frac{-2}{2} = -1[/tex]
Center ( 2, -1)
Equation of the circle
( x - 2)² + (y + 1)² = 34
