1.

Find a point which is equidistant from the points `A(-5,4)andB(-1,6)` How many such points are there ?

Answer» Let P (x,y) be the required point.
Given that, `" " PA-PB`
`implies" "PA^(2)=PB^(2)`
`implies" "(x+5)^(2)+(y-4)^(2)=(x+1)^(2)+(y-6)^(2)`
`implies" "x^(2)+10x+25+y^(2)-8y+16=x^(2)+2x+1+y^(2)-12y+36`
`implies" "8x+4y+4=0`
`implies" "2x+y+1=0`
It shows that infinite points are equidistant from AB because all points on perpendicular bisector of AB will be equidistant from AB.
One such point is the mid-point of AB.
which is `((-5-1)/(2),(4+6)/(2))=(-3,5)`


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