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Question Number 75276 by vishalbhardwaj last updated on 09/Dec/19
Write the formula of a circle if coordinates  of ends of diameter of the circle are given ?
$$\mathrm{Write}\:\mathrm{the}\:\mathrm{formula}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{if}\:\mathrm{coordinates} \\ $$$$\mathrm{of}\:\mathrm{ends}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{are}\:\mathrm{given}\:? \\ $$
Commented by mr W last updated on 09/Dec/19
(x−((x_1 +x_2 )/2))^2 +(y−((y_1 +y_2 )/2))^2 =(((x_1 −x_2 )^2 +(y_1 −y_2 )^2 )/4)
$$\left({x}−\frac{{x}_{\mathrm{1}} +{x}_{\mathrm{2}} }{\mathrm{2}}\right)^{\mathrm{2}} +\left({y}−\frac{{y}_{\mathrm{1}} +{y}_{\mathrm{2}} }{\mathrm{2}}\right)^{\mathrm{2}} =\frac{\left({x}_{\mathrm{1}} −{x}_{\mathrm{2}} \right)^{\mathrm{2}} +\left({y}_{\mathrm{1}} −{y}_{\mathrm{2}} \right)^{\mathrm{2}} }{\mathrm{4}} \\ $$
Commented by ajfour last updated on 09/Dec/19
(x−x_1 )(x−x_2 )+(y−y_1 )(y−y_2 )=0
$$\left({x}−{x}_{\mathrm{1}} \right)\left({x}−{x}_{\mathrm{2}} \right)+\left({y}−{y}_{\mathrm{1}} \right)\left({y}−{y}_{\mathrm{2}} \right)=\mathrm{0} \\ $$

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