Question

The number of points which is equidistant from the point (-5,4) and (-1, 6) is

Answer 1

There are infinite points, which are equidistant from (-5,4) and (-1,6)
The locus of such points is =
$using \: distance \: formula \\ {(x + 5)}^{2} + {(y - 4)}^{2} = {(x + 1)}^{2} + {(y - 6)}^{2} \\ {x}^{2} + 10x + 25 + {y}^{2} - 8y + 16 = {x}^{2} + 2x + 1 + {y}^{2} - 12y + 36 \\ 8x + 4y + 4 = 0 \\ 2x + y + 4 = 0$
Hence, the locus is straight line.
Hope it may help you !!!!!

Answer 2

there are infinite points