Question

find the locus of the point p for which distance from p to (4,0)is double the distance from p to x
-axis​

Answer 1

Step-by-step explanation:

Let the point is P(h,k)

Distance of P from origin =

(h−0)

2

+(k−0)

2

=

h

2

+k

2

Distance of P from the point (1,2) =

(h−1)

2

+(k−2)

2

=

h

2

+1−2h+k

2

+4−4k

=

h

2

−2h+k

2

−4k+5

Now,

h

2

+k

2

=2

h

2

−2h+k

2

−4k+5

Squaring both sides,

h

2

+k

2

=4(h

2

−2h+k

2

−4k+5)

h

2

+k

2

=4h

2

+4k

2

−8h−16k+20

3h

2

+3k

2

−8h−16k+20=0

So, the locus of P is

3x

2

+3y

2

−8x−16y+20=0