Question

find the equation of locus of a point which moves such that its distance from point (1,-2) is half its distance from X-axis​

Answer 1

Answer

Let the point be P(h,k)

PO be the distance from the origin

PO=

(h−0)

2

+(k−0)

2

=

h

2

+k

2

PA be the distance from x axis

Equation of x axis is y=0

PA=

0

2

+1

2

0(h)+1(k)+0

=k

Given PA=

2

1

PO

2PA=PO

2k=

h

2

+k

2

4k

2

=h

2

+k

2

h

2

=3k

2

Replacing h by x and k by y

x

2

=3y

2

is the required locus.