First slide

Definition of a circle

Question

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

Moderate

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

Solution

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 $2 x - 5 y + 11 = 0$

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