Answer:
(x + 4)² + (y + 5)² = 73
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 4, - 5), thus
(x - (- 4))² + (y - (- 5))² = r², that is
(x + 4)² + (y + 5)² = r²
The radius is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 4, - 5) and (x₂, y₂ ) = (4, - 2)
r = [tex]\sqrt{(4+4)^2+(-2+5)^2}[/tex]
= [tex]\sqrt{8^2+3^2}[/tex]
= [tex]\sqrt{64+9}[/tex] = [tex]\sqrt{73}[/tex] ⇒ r² = 73, thus
(x + 4)² + (y + 5)² = 73 ← equation of circle
Answer: [tex](x+4)^{2} +(y+5)^{2} = 73[/tex]
Step-by-step explanation:
the formula for finding equation of circle is given as :
[tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex]
where ( a,b) is the coordinate of the center and r is the radius
The radius is the distance between the point and the center , the formula for calculating the distance between two points is given by :
d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
d = [tex]\sqrt{(4-(-4))^{2}+(-2-(-5))^{2}}[/tex]
[tex]d = \sqrt{(4+4)^{2}+(-2+5)^{2}}[/tex]
[tex]d = \sqrt{8^{2}+3^{2}}[/tex]
[tex]d = \sqrt{73}[/tex]
since "r" is the distance , then
[tex]r = \sqrt{73}[/tex]
The the equation of the circle , using the formula [tex](x-a)^{2}+(y-b)^{2} = r^{2}[/tex] , will be
[tex](x+4)^{2} +(y+5)^{2} = 73[/tex]
