A point P on the y-axis is at the same distance from \(A(-5,\,-2)\) and \(B(3,\,2)\). What are the coordinates of P?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \((0,\,-2)\)
A point on the y-axis has x-coordinate 0, so let \(P=(0,\,y)\). \(PA=PB\) is the same as \(PA^2=PB^2\).
\(PA^2=(0+5)^2+(y+2)^2=25+y^2+4y+4\)
\(PB^2=(0-3)^2+(y-2)^2=9+y^2-4y+4\)
\(25+4y=9-4y\)
\(8y=-16\), so \(y=-2\)
So \(P=(0,\,-2)\)
Check: \(PA^2=25+0=25\) and \(PB^2=9+16=25\), so \(PA=PB=5\)
