The correct option is D ellipse
txa−yb+t=0 ⋯(1)
xa+tyb−1=0 ⋯(2)
From equations (1) and (2), the point of intersetion is
(h,k)≡(a(1−t21+t2),2bt1+t2)∴ha=1−t21+t2,kb=2t1+t2⇒h2a2+k2b2=(t2−1)2+4t2(1+t2)2⇒h2a2+k2b2=(t2+1)2(1+t2)2=1
Hence locus will be
x2a2+y2b2=1
Which is an ellipse.