Answer:
(x - [-1])² + (y - [-1])² = [13]
Step-by-step explanation:
If P and Q are the end-points of the diameter PQ, midpoint of the segment PQ will be the center of the circle. (Definition of the center of a circle)
Midpoint of a segment having extreme ends [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex]
Coordinates of the center = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Since, extreme ends of the diameter are P(-4, -3) and Q(2, 1)
Center of the circle = [tex](\frac{-4+2}{2},\frac{-3+1}{2} )[/tex]
= (-1, -1)
Radius of the circle = Distance between the center and Q,
Since distance between the two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Radius of the circle = [tex]\sqrt{(-1-2)^2+(-1-1)^2}[/tex]
= [tex]\sqrt{9+4}[/tex]
= [tex]\sqrt{13}[/tex]
Equation of the circle will be,
(x - h)² + (y - k)² = r²
Where (h, k) is the center and 'r' is the radius of the circle,
(x - [-1])² + (y - [-1])² = [13]
