Let a and b be non-zero and real numbers. Then, the equation (a x^2+b y^2+c ) (x^2-5 x y+6 y^2 )=0 represents

Step-by-step solution

Let a and b be non- zero real numbers. Therefore, the given equation (a x^2+b y^2+c ) (x^2-5 x y+6 y^2 )=0 implies either array rc & x^2-5 x y+6 y^2=0 & (x-2 y)(x-3 y)=0 & x=2 y and x=3 y array represent two straight lines passing through origin. Or a x^2+b y^2+c=0 When c=0 and a and b are of same signs, then aligned & a x^2+b y^2+c=0 & x=0 and y=0 aligned which is a point specified as the origin. When a=b and c is of sign opposite to that of a, a x^2+b y^2+c=0 represents a circle. Hence, the given equation (a x^2+