Suppose that the x -coordinates of the points A and B satisfy x^2+2 x-a^2=0 and their y -coordinates satisfy y^2+4 y-b^2=0 . Then, the equation of the circle with A B as its diameter is

Step-by-step solution

Let x₁ and x₂ are roots of equation x^2+2 x-a^2=0 and y₁ and y₂ are roots of equation y^2+4 b-b^2= (x-x₁ ) (x-x₂ )=0 and y^2+4 b-b^2 y₁, y₂= (y-y₁ ) (y-y₂ ) (roots of equation) Let A (x₁, y₁ ) and B (x₂, y₂ ) . Now, the equation of circle with diameter A B is given by (x-x₁ ) (x-x₂ )+ (y-y₁ ) (y-y₂ )=0 aligned & x^2+2 x-a^2+y^2+4 y-b^2=0 & x^2+y^2+2 x+4 y=a^2+b^2 & x^2+y^2+2 x+4 y-a^2-b^2=0 aligned