Answer:
(x - 10)² + y² = 29
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) = (10, 0), thus
(x - 10)² + (y - 0)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 ) = (10, 0) and (x₂, y₂ ) = (5, 2)
r = [tex]\sqrt{(5-10)^2+(2-0)^2}[/tex]
= [tex]\sqrt{(-5)^2+2^2}[/tex]
= [tex]\sqrt{25+4}[/tex] = [tex]\sqrt{29}[/tex]
Thus
(x - 10)² + (y - 0)² = ([tex]\sqrt{29}[/tex] )², that is
(x - 10)² + y² = 29 ← equation of circle
