(B) The equation of the chord of a circle with a given midpoint $(x_1, y_1)$ is given by $T = S_1$. Here,the circle is $S: x^2 + y^2 - 8x = 0$. The mi

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(B) The equation of the chord of a circle with a given midpoint $(x_1, y_1)$ is given by $T = S_1$. Here,the circle is $S: x^2 + y^2 - 8x = 0$. The midpoint is $(x_1, y_1) = (4, 3)$. $T = x(4) + y(3) - 4(x + 4) = 4x + 3y - 4x - 16 = 3y - 16$. $S_1 = (4)^2 + (3)^2 - 8(4) = 16 + 9 - 32 = -7$. Equating $T = S_1$,we get $3y - 16 = -7$. $3y = 9$,which simplifies to $y = 3$.

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

Medium

Which equation of the chord bisects the circle $x^2 + y^2 = 8x$ at the point $(4, 3)$?

A
$3y = 1$
B
$y = 3$
C
$4x - 3y = 9$
D
None of these

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Which equation of the chord bisects the circle $x^2 + y^2 = 8x$ at the point $(4, 3)$?

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