(C) In $\triangle ABC$,since $\angle A = 90^{\circ}$,the side $BC$ acts as the diameter of the circumcircle. Given the endpoints of the diameter are $

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(C) In $\triangle ABC$,since $\angle A = 90^{\circ}$,the side $BC$ acts as the diameter of the circumcircle. Given the endpoints of the diameter are $B(2, -4)$ and $C(1, 5)$,the equation of the circle is given by $(x - x_1)(x - x_2) + (y - y_1)(y - y_2) = 0$. Substituting the coordinates: $(x - 2)(x - 1) + (y - (-4))(y - 5) = 0$ $(x^2 - x - 2x + 2) + (y^2 - 5y + 4y - 20) = 0$ $x^2 + y^2 - 3x - y - 18 = 0$. Thus,option $C$ is correct.

Class 11 Mathematics 10-1.Circle and System of Circles Equations of circle

Medium

In $\triangle ABC$,$\angle A = 90^{\circ}$ and the coordinates of points $B$ and $C$ are $(2, -4)$ and $(1, 5)$. Then the equation of the circumcircle of $\triangle ABC$ is

AP EAMCET 2020 All AP EAMCET

A
$x^2+y^2+3x+y+18=0$
B
$x^2+y^2-3x+y-18=0$
C
$x^2+y^2-3x-y-18=0$
D
$x^2+y^2+3x-y+18=0$

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10-1.Circle and System of Circles

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In $\triangle ABC$,$\angle A = 90^{\circ}$ and the coordinates of points $B$ and $C$ are $(2, -4)$ and $(1, 5)$. Then the equation of the circumcircle of $\triangle ABC$ is

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