If all chords of the curve 2 x^2-y^2+3 x+2 y=0 , which subtend a right angle at the origin always passing through the point ( , ) , then ( , )=

Step-by-step solution

2 x^2-y^2+3 x+2 y=0 ...(i) Let y=m x+c be the chord y-m x c =1 Substitute in (i), aligned & 2 x^2-y^2+3 x(1)+2 y(1)=0 & 2 x^2-y^2+3 x ( y-m x c )+2 y ( y-m x c )=0 & (3 c-3 m) x^2+(2-c) y^2+(3-2 m) x y=0 aligned Chord is perpendicular to the curve So, the slope 3 c-3 m 2-c =-1 2 c-3 m=-2 Comparing with equation of chord y=m x+c(x, y)=(-3,-2)