Respuesta :
Answer:
Equation of the circle (x-3)²+(y-5)²=(6.4)²
x² -6x +9 +y² -10y +25 = 40.96
Step-by-step explanation:
Step(i):-
Given endpoints of diameter P(−2, 1) and Q(8, 9)
Centre of circle = midpoint of diameter
Centre = [tex](\frac{-2+8}{2} ,\frac{1+9}{2} )[/tex]
Centre (h, k) = (3 , 5)
Step(ii):-
The distance of two end points
PQ = [tex]\sqrt{(x_{2}-x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
[tex]PQ= \sqrt{(8+2 )^{2} +(8 )^{2} }[/tex]
PQ = √164 = 12.8
Diameter d = 2r
radius r = d/2
Radius r = 6.4
Final answer:-
Equation of the circle
(x-h)²+(y-k)² = r²
(x-3)²+(y-5)²=(6.4)²
x² -6x +9 +y² -10y +25 = 40.96
x² -6x +y² -10y = 40.96-34
x² -6x +y² -10y -7= 0
