The equation of a circle is x^2+y^2-6x-4y+4=0. i) Find the radius and centre of the circle. ii) Find the coordinates of the points of intersection with the line y=x+2

i) x² + y²- 6x - 4y + 4 = 0 x²- 6x + y² - 4y + 4 = 0 group the terms together x²- 6x = (x - 3)² - 9 factorise the x terms y² - 4y = (y - 2)² - 4 factorise the y terms x²- 6x + y² - 4y + 4 = (x - 3)² - 9 + (y - 2)² - 4 + 4 = 0 put them together(x - 3)² + (y - 2)² = 9 put constant terms on right side of equationCentre: (3,2) radius: 3
ii) x² + (x + 2)²- 6x - 4(x + 2) + 4 = 0 substitute y = x + 2 into the original equation x² + x² + 4x + 4 - 6x - 4x - 8 + 4 = 0 expand the brackets2x² - 6x = 0 simplify expression (cancel terms) x² - 3x = 0 simplify expression (divide by 2)x(x - 3) = 0 factorise equationx = 0 or 3 solve for xwhen x = 0, y = x + 2 = 2 substitute x values into line equation to get y valueswhen x = 3, y = x + 2 = 5points of intersection are (0, 2) and (3, 5)