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Question Number 87975 by ajfour last updated on 07/Apr/20

Commented by ajfour last updated on 07/Apr/20

Find radius of circle.

$${Find}\:{radius}\:{of}\:{circle}. \\ $$

Commented by Tony Lin last updated on 07/Apr/20

Commented by Tony Lin last updated on 07/Apr/20

(4/3)r=k(((4(√2))/3)r)^2   ⇒r=(3/(8k))

$$\frac{\mathrm{4}}{\mathrm{3}}{r}={k}\left(\frac{\mathrm{4}\sqrt{\mathrm{2}}}{\mathrm{3}}{r}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{r}=\frac{\mathrm{3}}{\mathrm{8}{k}} \\ $$

Commented by Tony Lin last updated on 07/Apr/20

Is the equation of parabola unknown?

$${Is}\:{the}\:{equation}\:{of}\:{parabola}\:{unknown}? \\ $$

Commented by ajfour last updated on 07/Apr/20

yes, must be   y=?x^2  .  ? to be determined..

$${yes},\:{must}\:{be}\:\:\:{y}=?{x}^{\mathrm{2}} \:. \\ $$$$?\:{to}\:{be}\:{determined}.. \\ $$

Commented by ajfour last updated on 07/Apr/20

I got kr=(3/4) , and there seems  (to me now), that something′s  wrong with this question (i thought  of myself..)

$${I}\:{got}\:{kr}=\frac{\mathrm{3}}{\mathrm{4}}\:,\:{and}\:{there}\:{seems} \\ $$$$\left({to}\:{me}\:{now}\right),\:{that}\:{something}'{s} \\ $$$${wrong}\:{with}\:{this}\:{question}\:\left({i}\:{thought}\right. \\ $$$$\left.{of}\:{myself}..\right) \\ $$

Commented by Tony Lin last updated on 07/Apr/20

yeah,m_(AD) =−((√2)/4)  y^′ ∣_(x=((4(√2))/3)r) =2kx=2k(((4(√2))/3)r)=((8(√2))/3)kr  ((8(√2))/3)kr=2(√2)  kr=(3/4)≠(3/8)

$${yeah},{m}_{{AD}} =−\frac{\sqrt{\mathrm{2}}}{\mathrm{4}} \\ $$$${y}^{'} \mid_{{x}=\frac{\mathrm{4}\sqrt{\mathrm{2}}}{\mathrm{3}}{r}} =\mathrm{2}{kx}=\mathrm{2}{k}\left(\frac{\mathrm{4}\sqrt{\mathrm{2}}}{\mathrm{3}}{r}\right)=\frac{\mathrm{8}\sqrt{\mathrm{2}}}{\mathrm{3}}{kr} \\ $$$$\frac{\mathrm{8}\sqrt{\mathrm{2}}}{\mathrm{3}}{kr}=\mathrm{2}\sqrt{\mathrm{2}} \\ $$$${kr}=\frac{\mathrm{3}}{\mathrm{4}}\neq\frac{\mathrm{3}}{\mathrm{8}} \\ $$

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