jee-advanced 2009 Q23

jee-advanced · India · paper2 Straight Lines & Coordinate Geometry Locus Determination
The locus of the orthocentre of the triangle formed by the lines $$\begin{aligned} &(1+p)x-py+p(1+p)=0\\ &(1+q)x-qy+q(1+q)=0 \end{aligned}$$ and $y=0$, where $p\neq q$, is
(A) a hyperbola
(B) a parabola
(C) an ellipse
(D) a straight line
The locus of the orthocentre of the triangle formed by the lines
$$\begin{aligned}
&(1+p)x-py+p(1+p)=0\\
&(1+q)x-qy+q(1+q)=0
\end{aligned}$$
and $y=0$, where $p\neq q$, is\\
(A) a hyperbola\\
(B) a parabola\\
(C) an ellipse\\
(D) a straight line