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

Question

The coordinates of the middle point of the chord cut-off by 2 x-5 y+18=0 by the circle x2+y2-6 x+2 y-54= 0 are (A) (1,4) (B) (2,4) (C) (4,1) (D) (1,1)

Tardigrade Admin · Accepted Answer

The midpoint is the intersection of the chord and perpendicular line to it from the center

(3, - 1)

.
The equation of perpendicular line is

5 x + 2 y - 13 = 0

.
Solving this with the given line, we get the point

(1, 4)

.

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

$(1, 4)$

$(2, 4)$

$(4, 1)$

$(1, 1)$

The midpoint is the intersection of the chord and perpendicular line to it from the center $(3, - 1)$ .
The equation of perpendicular line is $5 x + 2 y - 13 = 0$ .
Solving this with the given line, we get the point $(1, 4)$ .

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

(1,4)

(2,4)

(4,1)

(1,1)