A graph of $x=y^2$. The two points $P(10p,5p^2)$ and $Q(10q,5q^2)$ lie on this graph. The normals at $P$ and $Q$ intersect at the point $R$. Find the points $P$ and $Q$ on the graph of the inverse $y = x^2$
A graph of $x=y^2$. The two points $P(10p,5p^2)$ and $Q(10q,5q^2)$ lie on this graph. The normals at $P$ and $Q$ intersect at the point $R$. Find the points $P$ and $Q$ on the graph of the inverse $y = x^2$
?? You said P and Q lie on $\displaystyle x= y^2$ then you say "Find P and Q on the graph of the inverse $\displaystyle y= x^2$.
If P= $\displaystyle (10p, 5p^2)$ is on $\displaystyle x= y^2$ then we must have $\displaystyle 10p= 25p^4$ so either p= 0 or $\displaystyle 10= 25p^3$, $\displaystyle p^3= \frac{2}{5}$. If it were on $\displaystyle y= x^2$, then we would have to have $\displaystyle 5p^2= 100p^2$ which is only true for p= 0. Since R is not given I see no information derived from "the normals at P and Q intersect at R" except that they do intersect and are not parallel. The only way I could make any sense out of this is to say that P= Q= (0,0).