What are the coordinates of the center of the circle (x-1)²+(y-2)²=2² and y=2x+2?

Answer:Compare the given equation of the circle (x - 1)² + (y -2)² = 2²with standard form of circle: (x - h)² + (y - k)² = r²Here, (h, k) is the center of the circleand r is the radius of the circle.Thus, The center of the circle is: (1, 2)Also, for finding the point of intersections of (x - 1)² + (y -2)² = 2² and y = 2x + 2,Substitute the value of y from equation of line in the equation of circle.(x - 1)² + (2x + 2 - 2)² = 2²⇒ (x - 1)² + (2x)² = 2²⇒ x² + 1 - 2x + 4x² = 4⇒ 5x² - 2x - 3 = 0Applying Middle term splitting method5x² - 5x + 3x - 3 = 0⇒ 5x(x - 1) + 3(x - 1) = 0⇒ (5x + 3)(x - 1) = 0⇒ x = [tex]\frac{-3}{5}[/tex] and x = 1Thus, we get coordinates: [tex](\frac{-3}{5} ,\frac{4}{5} )[/tex] and (1, 4)