Find the condition on `a, b, c` such that two chords of the circle `x^2 + y^2 - 2ax - 2by+a^2 +b^2-c^2 = 0 `passing through the point `(a, b + c)` are bisected by the line `y = x.`

Find the condition on a and b for which two distinct chords of the hyperbola (x^(2))/(2a^(2))-(y^(2))/(2b^(2))=1 passing through (a,b) are bisected by the line x+y=b .

Find the condition on a and b for which two distinct chords of the hyperbola (x^2)/(2a^2)-(y^2)/(2b^2)=1 passing through (a , b) are bisected by the line x+y=b .

Find the condition on aa n db for which two distinct chords of the hyperbola (x^2)/(2a^2)-(y^2)/(2b^2)=1 passing through (a , b) are bisected by the line x+y=b .

Statement 1 the condition on a and b for which two distinct chords of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 passing through (a,-b) are bisected by the line x+y=b is a^(2)+6ab-7b^(2)gt0 . Statement 2 Equation of chord of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 whose mid-point (x_1,y_1) is T=S_1

Statement 1 the condition on a and b for which two distinct chords of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=2 passing through (a,-b) are bisected by the line x+y=b is a^(2)+6ab-7b^(2)gt0 . Statement 2 Equation of chord of the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 whose mid-point (x_1,y_1) is T=S_1

If two distnct chords of the circle x^2+y^2 -2x -4y=0 drawn from the point P (a,b) are bisected by y-axis then a) (b+2)^2>4a b) (b-2)^2>4a c) (b-2)^2>2a d) (b+2)^2>a

Find the condition that the straight line cx-by+b^(2)=0 may touch the circle x^(2)+y^(2)=ax+by