Does the point (-10,3) lie on the circle that passes through the point (-2,9) with center (-3,2)? Explain

Answer:yesStep-by-step explanation:The equation of a circle in standard form is(x - h)² + (y - k)² = r²where (h, k) are the coordinates of the centre and r is the radiushere (h, k) = (- 3, 2), so(x + 3)² + (y - 2)² = r²r is the distance from the centre to a point on the circleCalculate r using the distance formular = √ (x₂ - x₁ )² + (y₂ - y₁ )²with (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 circleSubstitute (- 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 = 50Hence (- 10, 3) lies on the circle