Answer:
(x - 5)² + (y - 7)² = 169
Step-by-step explanation:
The standard form of the equation of a circle 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) = (5, 7), thus
(x - 5)² + (y - 7)² = r²
The distance from the centre to a point on the circle is the radius
Calculate the radius using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (5, 7) and (x₂, y₂ ) = (10, 19)
r = [tex]\sqrt{(10-5)^2+(19-7)^2}[/tex]
= [tex]\sqrt{5^2+12^2}[/tex]
= [tex]\sqrt{25+144}[/tex] = [tex]\sqrt{169}[/tex] = 13, hence
(x - 5)² + (y - 7)² = 169 ← equation of circle
