A chord through the point (1,-2) cuts the curve 3 x^2-y^2-2 x+4 y=0 at P and Q . If P Q subtends an angle at the origin, then equals

Step-by-step solution

Given curve, 3 x^2-y^2-2 x+4 y=0 Chord passes through (1,-2) cut the given curve at P and Q Let slope of line P Q is m . Then, equation of line is aligned & y-y₁=m (x-x₁ ) & y+2=m(x-1) & y+2=m x-m & m x-y 2+m =1 & aligned Use Eq. (ii) in Eq. (i) as follows, aligned & 3 x^2-y^2-2 x ( m x-y 2+m )+4 y ( m x-y 2+m )=0 & 3(2+m) x^2-(2+m) y^2-2 x(m x-y) &+ 4 y(m x-y)=0 & x^2(6+3 m-2 m)-y^2(2+m+4)+x y &(4 m+2)=0 aligned General equation of curve is a x^2+2 h x y+b y^2+2 g x+2 f y+c=0 Compare Eqs. (iii) and (iv), a=6+m, b=