Question

FIND THE LOCUS OF POINT P SUCH THAT PA-PB=2 WHERE A(4,0) B(-4,0)

Answer 1

Answer:

It’s an ellipse with foci (0,2) and (0,−2) , centre (0,0) and eccentricity 23

This is because the foci are (0,±ae) if PA+PB=2a . and major axis is of length 2a [Fact from class 12]

PA2−PB2=(PA+PB)(PA−PB)

x2+(y−2)2−x2−(y+2)2=6(PA−PB)

−8y=6(PA−PB)

PA−PB=−4y3

PA=3−2y3

x2+(y−2)2=(3−2y3)2

x25+y29=1