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The coordinates of the middle point of the chord cut off by
$2 x - 5 y + 18 = 0$ on the circle $x^{2} + y^{2} - 6 x + 2 y - 54 = 0,$
are

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detailed solution

Correct option is A

The mid point is the intersection of the chord and perpendicular line on it from the centre (3, -1). The equation of the perpendicular line is 5x+2y-13=0. Therefore, the required point is (1, 4).

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The coordinates of the middle point of the chord cut off by 2x−5y+18=0 on the circle x2+y2−6x+2y−54=0, are

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Ready to Test Your Skills?

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The coordinates of the middle point of the chord cut off by
$2 x - 5 y + 18 = 0$ on the circle $x^{2} + y^{2} - 6 x + 2 y - 54 = 0,$
are