Answer:
yes
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) = (- 3, 2), so
(x + 3)² + (y - 2)² = r²
r 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 ) = (- 3, 2) and (x₂, y₂ ) = (- 2, 9)
r = [tex]\sqrt{(-2+3)^2+(9-2)^2}[/tex] = [tex]\sqrt{1^2+7^2}[/tex] = [tex]\sqrt{50}[/tex], hence
(x + 3)² + (y - 2)² = 50 ← equation of circle
Substitute (- 10, 3) into the left side of the equation and if equal to the right side then the point lies on the circle
(- 10, 3) : (- 10 + 3)² + (3 - 2)² = (- 7)² + 1² = 49 + 1 = 50
Hence (- 10, 3) lies on the circle
