AP EAPCET 23-Aug-2021 Shift 1 Paper

Given curve, 3x2−y2−2x+4y=0 ...(i)
Chord passes through (1,−2) cut the given curve at P and QLet 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°.