Question

Find the eqiuation of the locus of P, if A(4,0) and B(-4,0) and |PA-PB|=4​

Answer 1

Step-by-step explanation:

Given,

A=(4,0)≡(x

1

,y

1

),B=(−4,0)≡(x

2

,y

2

)

⇒∣PA−PB∣=4

Distance Formula =

(x−x

1

)

2

+(y−y

1

)

2

⇒

(x−4)

2

+(y−0)

2

−

(x+4)

2

+(y−0)

2

=4

⇒(x−4)

2

+y

2

=16+(x+4)

2

+y

⇒4x

2

+4+8x=x

2

+16+8x+y

2

⇒3x

2

−y

2

=12

⇒

4

x

2

−

12

y

2

=1