Answer:
(x + 1)² + (y - 1)² = 74
Step-by-step explanation:
See the attached figure.
The center of the circle is at (-1,1) and the radius is the distance between the points (-1,1) and (6,-4) {Since, (-1,1) is the center and (6,-4) is on the circle.
Now, radius, r = [tex]\sqrt{(- 1 - 6)^{2} + (1 - (- 4))^{2}} = \sqrt{74}[/tex]
Therefore, the equation of the circle is
(x + 1)² + (y - 1)² = (√74)²
⇒ (x + 1)² + (y - 1)² = 74 (Answer)
We know the distance between two given points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given by
[tex]\sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex].
