A B C D is a square with side 16 units and A is the origin. If the equation of the circle circumscribing the square A B C D is x^2+y^2=4 k(x+y) , then k=

Step-by-step solution

A B C D is a square with side 16 units let a=16 units Centre of the circle O ( a 2 , a 2 ) A C= (a-0)^2+(a-0)^2 = 2 a So, radius of circle = A C 2 = 2 a 2 = a 2 Equation of circle array rlrl & (x- a 2 )^2+ (y- a 2 )^2 & = ( a 2 )^2 x^2+ a^2 4 -a x+y^2+ a^2 4 -a y & = a^2 2 & x^2+y^2-a x-a y =0 & x^2+y^2 =a(x+y) here & a =16 & x^2+y^2 =16(x+y) & x^2+y^2 =4.4(x+y) by comparing & k =4 array