Question

find the equation of locus of a point which moves so that its distance from (-1,3) is always 8​

Answer 1

Answer:

Let the point be P(h,k)

Given point be A(a,0)

PA=

(h−a)

2

+(k−0)

2

Distance of P from y axis be PB

Equation of y axis is x=0

PB=

1

2

+0

2

1(h)+0(k)+0

=h

Given PA=4PB

(h−a)

2

+(k−0)

2

=4h

(h−a)

2

+(k)

2

=16h

2

h

2

+a

2

−2ah+k

2

=16h

2

15h

2

−k

2

−a

2

+2ah=0

Replacing h by x and k by y

15x

2

−y

2

−a

2

+2ax=0

15x

2

−y

2

+2ax=a

2

is the required equation of locus