If the chord of contact of tangents from a point (A ) to a given circle passes through (B ), then the circle with (A B ) as a diameter will ____

Step-by-step solution

Let an equation of circle (x^2+y^2+2 g x+2 f y+c=0 and point A (x₁, y₁ ) ) Then equation of chord of contact is ( aligned x x₁+y y₁+g (x+x₁ )+f (y+y₁ )+c & =0 (x₁+g ) x+ (y₁+f ) y+ (g x₁+f y₁+c ) & =0 aligned ) Let another point (B (x₂, y₂ ) ) through which chord (i) passes, so (x₁ x₂+g x₂+y₁ y₂+f y₂+g x₁+f y₁+c=0 (ii) ) Now equation of circle having (A B ) as diameter is ( aligned & (x-x₁ ) (x-x₂ )+ (y-y₁ ) (y-y₂ )=0 & x^2+y^2- (x₁+x₂ ) x- (y₁+y₂ ) y +x₁ x₂+y₁ y₂=0 (iii) aligned ) By the circles (x^2+y^2+2 g x+2 f