Question-174816

Question Number 174816 by aupo14 last updated on 11/Aug/22

Commented by a.lgnaoui last updated on 13/Aug/22

the folowing anser 2/2 wil be sent is in the next anser

$${the}\:{folowing}\:{anser}\:\mathrm{2}/\mathrm{2}\:{wil}\:{be}\:{sent}\:{is}\:{in}\:{the}\:{next}\:{anser}\: \\ $$

Answered by MikeH last updated on 12/Aug/22

That is because the intersecting points which lie on both circles also lie on the straight line obtained when the equations are subtracted. that is , if the intersecting points are P(x_1 ,y_1 ) and Q(x_2 ,y_2 ). this points also lie on y = mx+c, which is obtained when both equations of the circle are subtracted.

$$\mathrm{That}\:\mathrm{is}\:\mathrm{because}\:\mathrm{the}\:\mathrm{intersecting}\:\mathrm{points}\:\mathrm{which} \\ $$$$\mathrm{lie}\:\mathrm{on}\:\mathrm{both}\:\mathrm{circles}\:\:\mathrm{also}\:\mathrm{lie}\:\mathrm{on}\:\mathrm{the}\:\mathrm{straight} \\ $$$$\mathrm{line}\:\mathrm{obtained}\:\mathrm{when}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{are}\:\mathrm{subtracted}. \\ $$$$\mathrm{that}\:\mathrm{is}\:,\:\mathrm{if}\:\mathrm{the}\:\mathrm{intersecting}\:\mathrm{points}\:\mathrm{are} \\ $$$${P}\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} \right)\:\mathrm{and}\:{Q}\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2}} \right).\:\mathrm{this}\:\mathrm{points}\:\mathrm{also}\:\mathrm{lie}\:\mathrm{on} \\ $$$${y}\:=\:{mx}+{c},\:\mathrm{which}\:\mathrm{is}\:\mathrm{obtained}\:\mathrm{when}\:\mathrm{both}\:\mathrm{equations} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{are}\:\mathrm{subtracted}. \\ $$

Commented by a.lgnaoui last updated on 13/Aug/22