The locus of the middle points of the chords of the circle $x^{2} + y^{2} = 4$ which pass through $(3, 4)$ is

x^{2} + y^{2} + 4 x + 3 y = 0

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x^{2} + y^{2} - 4 x - 3 y = 0

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x^{2} + y^{2} - 3 x - 4 y = 0

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x^{2} + y^{2} + 3 x + 4 y = 0

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Solution

The correct option is C $x^{2} + y^{2} - 3 x - 4 y = 0$
equation of chord $\Rightarrow T = S_{1}$
$x h + y k - 4 = h^{2} + k^{2} - 4$
$x h + y k = h^{2} + k^{2}$ passes through $(3, 4)$
$3 h + 4 k = h^{2} + k^{2}$
$x^{2} + y^{2} - 3 x - 4 y = 0$

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The locus of the middle points of the chords of the circle x2+y2=4 which pass through (3,4) is

The correct option is C x2+y2−3x−4y=0equation of chord ⇒T=S1xh+yk−4=h2+k2−4xh+yk=h2+k2 passes through (3,4)3h+4k=h2+k2x2+y2−3x−4y=0

The locus of the middle points of the chords of the circle $x^{2} + y^{2} = 4$ which pass through $(3, 4)$ is

The correct option is C $x^{2} + y^{2} - 3 x - 4 y = 0$
equation of chord $\Rightarrow T = S_{1}$
$x h + y k - 4 = h^{2} + k^{2} - 4$
$x h + y k = h^{2} + k^{2}$ passes through $(3, 4)$
$3 h + 4 k = h^{2} + k^{2}$
$x^{2} + y^{2} - 3 x - 4 y = 0$