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Question Number 154465 by Eric002 last updated on 18/Sep/21

Commented by Eric002 last updated on 18/Sep/21

$a c i r c l e r o l l s i n s i d e a p r a b o l a . d o e s t h e$ $c e n t e r o f t h a t c i r c l e a l s o t r a c e a p r a b o l a ?$ $f o n d i t s e q u a t i o n$
Commented by MJS_new last updated on 18/Sep/21
$parabola: y=ax^2 circle with radius r p∈R line: { ((x=p−((2arp)/( (√(4a^2 p^2 +1)))))),((y=ap^2 +(r/( (√(4a^2 p^2 +1)))))) :} the parabola has a minimum radius of (1/(2a)) if r>(1/(2a)) the line has a loop anyway it′s never a parabola for r≠0$
$parabola : y = {a x}^{2}$ $circle with radius r$ $p \in R$ $line : {\begin{cases} x = p - \frac{2 a r p}{\sqrt{4 a^{2} p^{2} + 1}} \\ y = {a p}^{2} + \frac{r}{\sqrt{4 a^{2} p^{2} + 1}} \end{cases}$ $the parabola has a minimum radius of \frac{1}{2 a}$ $if r > \frac{1}{2 a} the line has a loop$ $anyway {it}^{'} s never a parabola for r \neq 0$
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