Given curve, 3x2−y2−2x+4y=0 ...(i) Chord passes through (1,−2) cut the given curve at P and Q
Let slope of line PQ is m. Then, equation of line is y−y1=m(x−x1) ⇒y+2=m(x−1) ⇒y+2=mx−m
mx−y
2+m
=1 ...(ii) Use Eq. (ii) in Eq. (i) as follows, 3x2−y2−2x(
mx−y
2+m
)+4y(
mx−y
2+m
)=0 ⇒3(2+m)x2−(2+m)y2−2x(mx−y)+4y(mx−y)=0 ⇒x2(6+3m−2m)−y2(2+m+4)+xy(4m+2)=0 ...(iii) General equation of curve is ax2+2hxy+by2+2gx+2fy+c=0 ...(iv) Compare Eqs. (iii) and (iv). a=6+m,b=−6−m This gives, a+b=0 ⇒ Angle subtended by these two lines at origin is 90°.