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` .

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 the set of 'K' for which two distinct chords of the ellipse (x^(2))/8+(y^(2))/2=1 passing through (2,-1) are bisected by the line x+y=K is [a,b] then (a+b) is…………

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 equation of that diameter which bisects the chord 7x+y-2=0 of the hyperbola (x^(2))/(3)-(y^(2))/(7)=1 .

Find the condition that line lx + my - n = 0 will be a normal to the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 .

If the line lx+my+n=0 touches the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . Then

Show that the midpoints of focal chords of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 lie on another similar hyperbola.

Show that the midpoints of focal chords of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 lie on another similar hyperbola.

If the normal at an end of latus rectum of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 passes through the point (0, 2b) then

The pole of the line lx+my+n=0 with respect to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , is