The locus of the center of the circles such that the point (2,3) is the midpoint of the chord 5 x+2 y=16 is

Question

The locus of the center of the circles such that the point (2,3) is the midpoint of the chord 5 x+2 y=16 is (A) 2 x-5 y+11=0 (B) 2 x+5 y-11=0 (C) 2 x+5 y+11=0 (D) none of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/112dcf6be9a7c5be3bf8af45d80f844e-.png" /> Slope of the given line =-(5/2) or ((5/2))((3+f/2+g))=-1 or 15+5 f=4+2 g Therefore, the locus is 2 x-5 y+11=0.

Q. The locus of the center of the circles such that the point $(2, 3)$ is the midpoint of the chord $5 x + 2 y = 16$ is

$2 x - 5 y + 11 = 0$

$2 x + 5 y - 11 = 0$

$2 x + 5 y + 11 = 0$

none of these

Slope of the given line $= - \frac{5}{2}$
or $(\frac{5}{2}) (\frac{3 + f}{2 + g}) = - 1$
or $15 + 5 f = 4 + 2 g$
Therefore, the locus is $2 x - 5 y + 11 = 0$ .

Q. The locus of the center of the circles such that the point (2,3) is the midpoint of the chord 5x+2y=16 is

2x−5y+11=0

2x+5y−11=0

2x+5y+11=0