at-h-2-a-t-k-2-R-2-where-a-h-k-R-are-constants-Then-find-s-2-t-1-t-2-2-1-1-t-1-2-t-2-2-where-t-1-t-2-are-roots-of-eq-at-top-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 48482 by ajfour last updated on 24/Nov/18

(at−h)^2 +((a/t)−k)^2 =R^( 2) where a, h, k, R are constants. Then find s^2 =(t_1 −t_2 )^2 (1+(1/(t_1 ^2 t_2 ^2 ))) where t_1 , t_2 are roots of eq. at top.

$$\left({at}−{h}\right)^{\mathrm{2}} +\left(\frac{{a}}{{t}}−{k}\right)^{\mathrm{2}} ={R}^{\:\mathrm{2}} \\ $$$${where}\:\:\:{a},\:{h},\:{k},\:{R}\:{are}\:{constants}. \\ $$$${Then}\:{find}\: \\ $$$$\:\:\:{s}^{\mathrm{2}} \:=\left({t}_{\mathrm{1}} −{t}_{\mathrm{2}} \right)^{\mathrm{2}} \left(\mathrm{1}+\frac{\mathrm{1}}{{t}_{\mathrm{1}} ^{\mathrm{2}} {t}_{\mathrm{2}} ^{\mathrm{2}} }\right)\: \\ $$$${where}\:{t}_{\mathrm{1}} ,\:{t}_{\mathrm{2}} \:{are}\:{roots}\:{of}\:{eq}.\:{at}\:{top}. \\ $$

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at-h-2-a-t-k-2-R-2-where-a-h-k-R-are-constants-Then-find-s-2-t-1-t-2-2-1-1-t-1-2-t-2-2-where-t-1-t-2-are-roots-of-eq-at-top-

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