Question

Consider the parabola $y=x^2$ in the $xy$-plane, with ' $O$ ' as the origin.
Right triangle $PQR$ is inscribed in the given parabola right angle at $Q$, with coordinates as $P(p$, $p2$ ) $Q\left(q,q^2\right)$ and $R\left(r,r^2\right)$, where $p,q$ and $r$ are non-zero integers. The value of $\frac{p+r}{q}$, is equal to

• A. 2
• B. -1
• C. 1
• D. -2

Answer 1

Answer: (D)

$m_{QP}\cdot m_{QR}=-1$
$(q+p)(q+r)=-1$. Sum is possible if
$q+p=1$ and $q+r=-1$; on adding $2q+p+r=0$
$\Rightarrow \frac{p+r}{q}=-2$.