The quadratic equation whose roots are the coordinates of the circumcentre of the triangle formed by the points (-2,-1),(6,-1)(2,5) is

Step-by-step solution

Equation of perpendicular bisector of line joining points A(-2,-1) and B(6,-1) is [ mid-point of A B is (2,-1)] and similarly equation of perpendicular bisector of line joining points B(6,-1) and C(2,5) is [ mid-point of B C is (4,2)] y-2= 4 6 (x-4) Now, point of intersection of perpendicular bisector is the circumcentre of A B C , so On solving Eqs. (i) and (ii), we get C (2, 2 3 ) . It is given that quadratic equation has roots are 2 and 2 3 , so equation of required quadratic equation is x^2- (2+ 2 3 ) x+2 ( 2 3