First slide

Definition of a circle

Question

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

Moderate

A

$(1, 4)$
B

$(2, 4)$
C

$(4, 1)$
D

$(1, 1)$

Solution

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 $5 x + 2 y - 13 = 0$ . Therefore, the required point is $(1, 4)$ .

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