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  4. Consider the parabola y=x2 in the x y-plane, with ' O ' as the origin. Right triangle PQR is inscribed in the given parabola right angle at Q, with coordinates as P ( p, p 2 ) Q(q, q2) and R(r, r2), where p, q and r are non-zero integers. The value of (p+r/q), is equal to

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Q. Consider the parabola $y=x^2$ in the $x y$-plane, with ' $O$ ' as the origin.
Right triangle $PQR$ is inscribed in the given parabola right angle at $Q$, with coordinates as $P ( p$, $p \quad 2$ ) $Q\left(q, q^2\right)$ 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

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Solution:

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

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