Answer:
The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²
or
The equation of the circle x² + 2 x + y² - 4 y = 15
Step-by-step explanation:
Given points end Points are p(-3,-2) and q( 1,6)
The distance of two points formula
P Q = [tex]\sqrt{x_{2} - x_{1})^{2} + ((y_{2} -y_{1})^{2} }[/tex]
P Q = [tex]\sqrt{1 - (-3)^{2} + ((6 -(-2))^{2} }[/tex]
P Q = [tex]\sqrt{16+64} = \sqrt{80}[/tex]
The diameter 'd' = 2 r
2 r = √80
= [tex]\sqrt{16 X 5}[/tex]
= [tex]4 \sqrt{5}[/tex]
r = 2√5
Mid-point of two end points
[tex](\frac{x_{1} + x_{2} }{2} , \frac{y_{1} +y_{2} }{2} ) = (\frac{-3+1}{2} ,\frac{-2 +6}{2} )[/tex]
= (-1 ,2)
Mid-point of two end points = center of the circle
(h,k) = (-1 , 2)
The equation of the circle
(x -h )² +(y-k)² = r²
(x -(-1) )² +(y-(2))² = (2(√5))²
x² + 2 x + 1 + y² - 4 y + 4 = 20
x² + 2 x + y² - 4 y = 20 -5
x² + 2 x + y² - 4 y = 15
Final answer:-
The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²
or
The equation of the circle x² + 2 x + y² - 4 y = 15
Answer:
Step-by-step explanation:
